For the Bb side of things, I play a modified Vincent
Bach Stradivarius #37 with a Monette STC-2 B12M mouthpiece
(not mine, just a stock photo of one)
For the C side, I use a Yamaha Heavy Wall with
a Monette STC-3 C12 mouthpiece.
(also not mine, just a stock photo of one)
I also have an unique cornet in my bag of tricks:
It's a Conn from the 1970s made by Yamaha while
Conn was moving it's plant.
Some parts of it look very much Conn, while others
are obviously Yamaha.
(photo currently not available)