Use the thick bottles to bottle with when using brett.
I would suggest not using priming sugar for the brett. I do not know your FG for the beer, but the brett will eat the residual maltose and produce c02. Adding priming sugar will either make the beer over carbonated or make the greater possibility of a bottle bomb. I just pulled a bretted dubbel that reached an fg of 1.008 from 1.017 within 7 months.
The key to getting the carbonation right is to let the bottles sit. Forget about them for at least 6-7 months. Keep them in a warmer area of the house 65-70. Pull a sample and it is not carbonated enough let them sit another two months. Brett is very very very slow to work.
The head that is produced by brett tends to be a little more rocky and light. Champagne is how i would describe it.
The key is to give it time and it will come out amazing.