I never used it myself, so I can't say for sure, but a quick search on deadlystream shows that they might have a conflicting script (it duplicates Bao-Dur during his training). Maybe there is something else, maybe not.
The mod is 20 years old, which predates first release of TSLRCM by a few years. I can’t test it myself right now, but you might find more details in older forum threads.

Do you know if SS Prestige Padawans is compatible with TSLRCM?

I won't, because the game engine doesn't support adding a third class to characters. But there’s already a mod that lets you train companions in prestige classes instead of basic Jedi ones.
Check it out: SS Prestige Padawans [www.gamefront.com]

Will you be adding this for the rest of the companions as well?