I've been gifted a pair of Thiel CS2s

I get it, this is Audiogon; sell them, and get appropriate speakers for the room.

I ran the same speakers for many years, in various rooms. Your room is too small. Perhaps something like Thiel's SCS's might work.

One needs to sit at least 8' from the speakers. The speakers need to be at least 1' from the walls and at least 3' from the corners.
The room has to be able to accommodate greater than 40 Hz bass extension.
IME, the Thiel CS 2's ported bass is a bit looser than most other Thiels, the high end can sound hard if they're toed in towards the listener. This room appears as though it could exaggerate those bass issues, and the nearness of the side walls practically demand toe in to avoid the early reflections that the Thiels wide sound-stage is likely going to aggravate otherwise.
Being nearly a cube, and being so small this room is going to be problematic with most speakers, but CS 2's will most likely highlight these issues.
On the other hand the Theil CS 2's with their 6 Ohm nominal, 5 Ohm minimum impedance, and 87 dB sensitivity are perhaps Thiels easies amplifier load (though IME the CS 2's sonic signature does require careful amplifier selection), and are reputed to be Thiel's most durable product ever.

Thanks for reminding me, yes, the Thiels should to be at least 8' apart from each other as well. Ideally they would be 10' apart from each other, 10' from the listener, >5' from the side walls and >3' from the wall behind the speakers.

Thiel's own SCSs are a much better fit for this room.

Well, that changes things quite a bit, still a tight fit, not quite ideal, but it can work.
IME, the McCormack amps though very fine amps in their own right, and excellent with other speakers, are a bit too forward and shouty with the Thiel CS 2's.
With your budget, I'd consider a Forte' or conrad-johnson solid state amp. Either manufacturer's pres in either ss or tube would work nicely too.
My experience with an Electrocompaniet integrated was pleasurable, though ultimately just a bit dark on top for my tastes.

Doggiehowser, My money is with my direct experience of over a decade with the the CS 2's without concentric drivers, rather than with your recollection of your friends CS 2.4's with concentric drivers, in an undersized space.
Would you not exchange an over-sized gifted sweater for an appropriately sized one?

Some good thougts from Newbee.