Best Headphone system under $1000???

I really like my old Stax Electrostatic headphones and their amp to drive them.    I'll admit I am biased toward them, but it wouldn't hurt you to start your listening / shopping experience with them and move on from there.  

Do check out headphone systems at twice your budget so you know what you are missing out, if anything.   At least, if you do discover the difference, you can make an honest judgement. 

Be careful though, it is very common  to do permanent hearing damage with headphones as pumping too much SPL in the tiny ear canal is easy to do.
For open back headphones, in general if you can't carry on a conversation with someone in a normal voice at 3 to 4 feet, the phone volume is too loud.  Turn it down!

I'm not sure if it's reasonable to expect to "replicate" what you have in a headphone system, the experience of listening to music through speakers and headphones is very different.  Your budget allows for some decent components. 

If you're willing to buy used, consider the Audeze LCD-2.  They are detailed, but on the warm side and have good bass and will sound great with the types of music you enjoy.  You can get some new earpads for a set of used of headphones if you're squeamish about buying used.  The Audeze ones are about $100, there are some nice aftermarket ones out there for less.

If you prefer new, check out the Hifiman HE-560.  They are similar to the LCD-2, but are harder to drive and will require a more powerful headphone amp.  Another great set of headphones is the Focal Elear (or Elex from Massdrop).  These are more "neutral" than the other two I've mentioned, but are very detailed and easy to listen to.

An outstanding headphone value that I recommend looking at is the Massdrop Sennheiser HD-6XX headphones.  These are super comfortable and sound great and are only $200.

Like speakers, the headphone is going to impart more to the sound signature than the amp, but proper amplification is important.  I don't have any suggestions in your budget range, most of my amps cost more than that.  If you can find a used  Musical Fidelity M1-HPA or M1-HPAP, that's an inexpensive amp that I have owned that has a lot of power and sounds good.

The system I use and can therefore recommend is Focal Elears and Schiit Jotunheim.

The system I use and can therefore recommend is Focal Elears and Schiit Jotunheim.

I was going to mention Schiit, but I'm not familiar with the models that would fit in the OP's budget.  I have a Mjolnir 1 and it's a great amp.  If the Jotunheim is close in terms of sound quality and performance, that's definitely a good option to consider.

Grado RS-1 or RS-1i or RS-1e Reference headphones plus Grado headphone amp, either battery powered or not.
A little over $1k new but it should do it.

Get the Beyerdynamic DT 1990 Pros, with a  Monolith by Monoprice Desktop Headphone Amplifier and DAC with THX AAA Technology (Dual AKM 4493 DACs & Dual AAA-788 Modules)

These 2 come in at $1100 total, but you CANNOT do better than this combo at that price

Beyer Dynamics T1
Sennheiser HD 800
If you have an old receiver or integrated with a headphone jack, use that until you save another $800-$1000 for an amp.

I believe there are some trickle-down technology benefits from some of the companies that offer megabuck phones, i.e. Focal, Hifiman, Sennheiser and others, in their lesser-priced models. I would start with used phones in my price range and move up from there. Try to hear as many as possible before buying the pair you will probably use for many years. In my experience, I started with Stax Lambda, moved up to Lambda Pros years later, and now use Stax 009s w/T1S tube driver unit. Again, try to buy phones you believe you can live with for many years. You can always upgrade later by adding a dedicated tube amplifier when your budget expands.

JDS Labs Atom as the amp: $100 (almost as good as the THX 789).  
Topping D10 as the DAC: $90 (or Schiit Modi 3 for $100).  
  
Leaving $900: 
Well, at $1000 the HiFiMan Ananda are good, or if you don’t mind used, see what others are selling. The Focal Elsar are $650 and supposed to be awesome.

I can help you. I have owned a ton of headphones. 

The probelm with going over to forums like head-fi is a lot of the people do not have any good two channel experiance for reference and get used to the colored sound of headphone and make questionable recommendations, Imo of course...

Your Vandersteen 2CE Sig will be far more neutral than a musical set of headphones. A lot of the popular headphones now are crazy dark so you might need a more neutral headphone than you think. 

Anyway I would without hesitation recommend the Focal Elex for $700. It is from a company called mass drop that does bulk buys and adds some of their own design changes. It basically sounds the same as the $1500 focal clear but with a hint less sub bass. 

It has the technicalities to hang or better headphones in the $1000-$2000 range. I also own the HD800S $1700, LCD-X $1200), Grado PS500e $600 and I would choose the Elex as my only headphone if I had to. 

The tonal balance of the Elex is that the bass from 30-150 has about a 3 dB boost and the highs are very detailed but a little shelved down. Some would call them neutral in the highs but I would not. The mids have a slight rise at 1-2k so vocals pop out a bit which is nice. They are easy to drive and can run off an iPhone but still scale well with good electronics. 

The Elex have more bass and softer highs than my Thiel 2.4 for reference, and tonally I would say is close to the sonus faber Olympica iii. A little round and a little soft with leading edge impact in the sub base but very very good at the same time everywhere else. 

https://www.massdrop.com/buy/massdrop-x-focal-elex-headphones?mode=shop_open&utm_source=shopping...

Some quick comments below. 

HD800S (used in your price range), weak bass and recessed mids can make these sound thin and bright. Crazy good soundstage. Almost as good as a near field speaker setup. But I would pass based on your comments for musical tates. 

LCD-2C. Very rolled off highs but ruler flat from 20hz-1k. Crazy good sub bass with great leading edge sub bass impact. Pretty soft everywhere else though. Think magnepan softness...  the vocals sounded wonky to me and I could not get passed it. The LCD-X sounds about the same with more balanced highs (still shelved down) and about twice the price. They also have odd mids and I can’t realy recommend them unless you value bass detail/impact above all else. 

Grados, a hard pass for your tates. Very aggressive sound with forward mids and highs. Bass rolls off early. I really like the PS500e (darkest of the grados, still bright) but is easily outclassed on technicalities by these other headphones. 

Sennhieser HD650/HD660s. The long running reference headphone any only $300ish. Mass drop sells a version for $200 I think. They are good but a little boring and lack impact/dynamics. The Elex is turned about the same and much punchier and fleshed our across the entire frequency range. With a VERY good amp you can get dynamics out of the HD650 but not worth the effort. The Elex is already dynamic...

So all in all I would choose the Focal Elex for a good balanced yet warm sound with good sound stage only bettered by the HD800S sound stage. The LcD-2C or X if you value great sub bass and bass definition above other technicalities, HD650 if you want something cheep and already own a good amp.

Wow guys! I truly value all of your feedback! 
I’m definitely checking out all of the possibilities that are available on Massdrop. It seems like a great place for dipping my toe in the headfi pool. 
The Focal cans and the Sennheisers were two that I was looking at closely. 
James63- I especially appreciate your way of comparing different cans to speakers I’m familiar with. My initial impulse was to get Massdrop HD6xx and pair them with the Massdrop Cavalli CTH headphone tube amp. Has anyone heard this combo?
Net cost for above would be $550. 
However, the Elear and Elex has piqued my interest. Especially if I could drive them with my iPhone X when I want to be portable. 
I have a decent DAC already- MHDT Stockholm 2. 
Any further advice or suggestions is most welcome. 

I owned the HD650 and ran them off of a Benchmark DAC2 HDR which has a pretty high power class A amp in it. The combination was pretty boring and lacked dynamics. The lack of dynamics is the biggest issue for a speaker guy. No headphone gets it right. Just something that comes with the territory. I have not heard the mass drop amp. 

For me me personally I would take the Focals Elex on a mid priced amp over the HD650s (same as the HD6XX I believe). Some people run the hd650s on crazy expensive amps and they say it helps but it is just not for me. The focals get up and go even out of a phone (but need a better amp to pull out all the details and soundstage).

 I just use a chord mojo and phone these days for my headphones. Desk top stuff sounds better I guess but not as much as you would think. Just depends on if you listen to the details or the music...

Do NOT buy the focal Elear. It is terrible! Worst headphone I have ever owned. It has a 25db dip in the upper mids and is super bassy. I hated it when I owned it. Oddly the Focal Elex is just the Elear with pads from the focal clear more or less and it sounds totally different. It is like putting your speakers in a very bad room then moving to a very good room. 

I agree with the comparison between the Elex and the HD-6XX, but would not call the HD-6XX boring.  I guess one man's smooth and easy to listen to is another man's boring. The Elex is definitely better, but the HD-6XX is a lot of headphone for the money. What I like most about the HD-6XX is how light and comfortable they are.

Stax L300 Limited Edition would be my vote for under 1k with an energizer.

Big_greg

Agreed and good point. I think a lot of classical guys would appreciate the HD650/HD6XX and they are a steel. They were $350 10 years ago and they might even be cheaper now. I wish the same could be said about the speaker market prices...

@james63 The HD-6XX are $199.