This is an issue that I have thought much about as well. I also currently use a ss processor (B&K) and a 5-channel budget amp (Adcom) but also a Counterpoint ss amp for the front speakers with much refinement over the Adcom. And I too have Talon speakers (Khorus in front and Peregrine in back). The system is fairly good but definitely in the sterile zone compared to my all tubed music system in another room.
I tend to agree with Nsgarch's comments in these forums but I would typically not run with tube amps in a HT system ..... especially if it doubles as the home's primary TV setup. Tube amps can generate a lot of heat and they become VERY costly to maintain; their reliability can be an issue due to tube failures, etc. So only if this system was not on all the time would I even consider tube amps here. And it seems like such a waste for movies/tv anyway.
Time and time again I have found the make or break link in a music system to be a tube preamp. And unfortunately, only a handful of models out there even cut it for me. This is very different than having heard and enjoyed some very good amplifiers, including many ss. So if you are looking to resolve the "sterile" issue, the tube preamp is the direction I would go.
I also looked into finding a tube preamp with HT bypass that would link the inputs directly to the outputs through a switch AND not require the unit to be on...and thus conserve tube life. But so far no luck. I had heard rumors the Modwright had this feature but Dan Wright wrote to me that his preamp did not support this. So if you end up with a tube preamp, it will most likely be on all the time and generating a little heat.
You can go very far for $4k. I would look to put half into a tube preamp and the other half in an amp for the front channels. The Modwright 9.0 line stage gets a lot of praise here in the $2k zone. And I believe there is a phono option for these. If you want to get less in cost, the BAT VK3 series is another model that has an optional phono board.
As for amps, something like a used Ayre V5 or V3, Bel 1001, McCormmack 125/225 would be what I would look into. And with the Talons having 90ish db sensitivity, they really rock without the need for super high powered amps.