Ok, from what you write it seems there is a fair amount of technology which comes only from The Republic and no other races.
If that is the case all components should be of Republic's origin.
You could of course add some components of the The Brotherhood which have minor tweaks to distinguish them from those of the Republic.
What about ship's hulls?
Has the Brotherhood developed sufficent technology to build new ones ?
Has the Brotherhood a technology at all? They don't seem the likes who spend their time in a laboratory researching things!
From what you write it seems that during the wars they mainly captured disabled Republic's ships or just acquired fleets they found on revolting planets.
Otherwise they could have their own hulls to let us players better tell friends from foes during battles.