Personally, I like the idea of going front to back, myself. Source, preamp, amp, speakers... either way however leads to a positive end, eventually.
Interjecting a new source, int. or pre & amp is going to be quite a shift in performance! Adding on the necessary cabling after that will also be quite an addition.
I think you are right in looking at just a source/CDP & an integrated amp... for now. Having a source which provides all of the info the signal has right off is way important! That's what the rest of the ritg is going to be working with afterall.
The deal between tubes and SS is simple.... SS is no better or worse than would be hollow state subjectively speaking. Tubes, do offer more options for the ears, via some tube rolling. So that has to be a consideration if you enjoy tweaking or just making simple changes to the sound systems signature from time to time.
The main thing is toting along your speakers if at all possible... or arranging an in home trial. That part comes only after you are certain you wish to deal with ... whomever you pick of the dealers you meet.
I don't see any of your listed possibilities as bad ones either. I would say though if you are in no rush or that $3K isn't burning a hole in your pocket to go slower. A CDP seems in order though and Rega makes some good ones with good reviews. I'd get as good as I could there for now be it Rega or otherwise.
In fact all of your short list is well represented in the 'preowned' mkt as well and that would allow you to get better return on your available funds/budget... unless you gotta have brandy spankity new, used components sure helps one escalate the preformance level of one's rig.
In conjunction with a resolving source, ASL, Prima Luna, and with a bit of tube rolling, a Jolita int could do just what you are looking for... and if preowned, both power cords and cabling additions will be avaialable too.... and the wires are sure important. They are the icing so to speak, on the cake.
Tote your speakers, ask questions about warranty & other policies, look at the cabling being used too. Listening to $2K to $3K components connected with $2K worth of wires is something I'd like to know up front... also see if they're using a power conditioner during the audition. I've overlooked that last bit in the past myself... and it's a very common practice to use them during presentations.
So are aftermarket footers, iso cups, and these too make an impact on the sound.. so do open your eyes when auditioning so you know what's what. I'm sure you're astute enough here, but I've been overly zealous in the past myself when being on the verge of a whole new rig!
Again.. I would just go listen... look... ask... and get a nice CDP first.
Come back in a few weeks with it and plug it into the power train you like most and go from there... You've two known quanities then, speakers and source.
Good luck, take care, and just listen to the music that gets your attention.