Sorry Alex, I forgot about this thread...
I really don't have any experience with any of your gear, so I can't comment too much.
Even though my phono section is MM, it works very well with my Dynavector 10x5 (2.5 mV MC). If any cartridges you're contemplating have this or similar output, a Bryston MM section should be fine. I'm not the biggest expert on this, so I have to defer to someone else.
The Rega RB300 is an excellent tonearm, and should be fine with your choices. I've heard it with a 10x5, and it sounds excellent with it too. Keep in mind that the tonearm is only one part of the chain though.
I haven't heard anything made by Clearaudio, so I have no idea what their house sound is like to be able to say if the Bryston phono stage would or wouldn't be an improvement.
You may want to post this in the Bryston circle, as you'll probably get more opinions and experiences with their phono stages.