I owned CS 2's for many years and tried quite a few different amps with them. The CS 2's with their 6 Ohms nominal/ 5 Ohm minimum impedance, are probably the easiest of all Thiel speakers to run with tubes, but with your budget and what I perceive from your thread to what your seeking, your probably better off with ss.
The top end needs to be monitored, any amp with a rising or hot top end should be avoided. At the opposite end, the ported bass, though fairly well extended can be a bit soft.
Within your budget:
My first pick, if you could find one at a price you'd feel comfortable with is Threshold S/500, preferably one that has recently had new caps and re bias done by somebody reputable like Jon Soderberg of Vintage Audio Repair.
My second choice would be a conrad-johnson MF 2500 preferably with the A upgrade.
These speakers need quality amplification. don't be afraid to spend money on the amps. It might be a bit nonconventional to spend so much on the amp to speaker ratio, but the combination will yield results that reveal the true value of the combination.