what is my system's weakest link?

I agree that the Rega and the Thiels are probably not a good match. That said, I would probably replace the speakers first with something that is easier to drive. $1300.00 opens up a lot of possibilities on the used market. Specific recommendations would depend on your room and listening habits.

Shakey

Those Thiels would benefit from, and you would know it immediately, an amp supplying them with a stouter power supply.

the room, which it is for all systems.

I have a different take on this. The "weakest link" is the Project tt. The biggest "problem" is the Thiel/Brio combo. The Brio is a nice integrated and while you mention wanting a new pre, what will you do about a power amp? The C28 is a good vintage pre, but do you really want to open up that can of worms (restoration/reliability of pre, new power amp)? If it were me and the goal were the best possible sound for +$1000 or so, I would build a new system around the Brio which is a solid integrated, get friendlier speakers (I like the Vandersteen suggestion) which you should be able to buy with what you get for the sale of the Thiels plus a little more, and GET A BETTER FRONT END; something like this (no affiliation):

http://app.audiogon.com/listings/turntables-vpi-traveler-v1-2013-11-06-analog-90039

or even better:

http://app.audiogon.com/listings/turntables-exquisite-well-tempered-lab-record-player-optional-dust-cover-with-marigo-audio-lab-p-2013-11-02-analog-94925-corte-madera-ca

I think you will have infinitely more satisfying sound this way. Good luck.

Music Direct has some great process on Focal Chorus 800 series speakers. I have never heard a Focal speaker that I didn't like. The 816v is a fantastic choice in my opinion.