Avalon

Thank you all for advice here — and yes, it did take me an unusual amount of time to get back to this thread.

@rzado ADO — I have come to the conclusion that although the Rogue is a great and wonderful bargain in an amp, it may not be the best for the Eidolons. ...Sheesh, what a great hobby, eh? Never bypass an opportunity to tweak your sound. ...I am now looking at a new amp, perhaps Ayon Audio Triton III. I can not say enough about my Ayon CD-07, that really sold me on Ayon.

@reynolds853 — I have had great success with PS Audio PowerPlants, and yes I did install one into this system in question. Happy with that and completely convinced (once again) that power isolation/regeneration is a key to great audio.
The Rogue is running:
    4 x Tung Sol KT120
    3 x RCA clear tops 12AU7A
    2 x 12AX7 (not sure which tubes are in it right now...)
When I bought it second hand, the fellow who sold it to me gave me a mess of additional tubes to roll. Thats fun with this amp, plus the biasing is something every audiophile should do at some point).This is my first tube amp, and I was delighted (still am, it sounds great) but you know we congregate on audio forums for a reason: we ain't never satisfied for too long... 
This system is in my living room, I have two other systems at home — those both use Parasound amps... which are dead dead —dead I say— quiet. The Rogue is not dead quiet, which has set me upon my course toward a black background in the tube world. Am I nuts? (Yes, because you can't hear any noise at normal listening levels, only when there is no signal and you stick your ear into the speaker...)
So, I love the feel of tubes, and the Rogue is a great intro to this world. What next?

HI Vicweast,

I think you have reached the right decision.  The Ayon Audio Triton III should be a significant upgrade, and I certainly recommend you demo it if you have the opportunity (although you may need to run in pentode to really drive the Eidolons).  However, at that price (I believe the Ayon is $11k retail), there are three other options I would recommend you consider.  

First, for solid state, the Symphonic Line Kraftwerk and Kraftquelle integrated amps are exceptional pieces, will be dead quiet, and are very good pairings with the Avalons.  Second, also solid state, and reflecting your preference for Parasound, the JC-1 amps would also make a very good pairing with the Avalons, coupled with an appropriate preamp.  Finally, if you want a call it quits, "end of the line" system, get a used CAT amp and preamp (which you can get for ~$7-11k used), and you are done -  I have literally spent triple that price of that setup (i.e., Avalon and CATs) and not equaled the performance.

Best of luck.

@rzado The price of the Ayon Audio Triton III (pristine demo unit) was "too good to pass up"...

Vicweast - I hear you, and the Ayon is still a great choice; I am sure you will enjoy the combo.  Let us know how it works out; just watch out for your back when you pick it up - its pretty dang heavy.

Well, yesterday the FedEx truck came. The Ayon Triton III box weighed 133 pounds. I had help from the FedEx guy in getting the box into the front hall but from there...

It has been cold here and once I managed to lift the amp out of the box (when lifting it, its an ungainly monster that is back-side heavy) I let the electronics acclimate to the house for several hours. I also made a high-end zip-wire set of speaker cables and hooked it up to a set of nice but sacrificial Energy speakers. (I'm going to try to keep my Avalons from blowing up with new gear.) After the right amount of anticipation: The switch was flipped! 

I am quite happy with the initial results, so much that it only took another two hours to replace the Rogue amp with the Ayon!