Recently I joined a brass choir. Out of all the other people there, I play the quietest, and the director frequently reminds me of it. But when I play as loud as I ought to, I feel like it's too harsh and may end up doing more harm to my chops than anything. What sort of things could I do/practice to become better at playing at louder levels and projecting more?

Projecting and playing loudly are two different things.

In general to play more loudly without injuring yourself I woudl suggest playing long tones. Start soft, crescendo to loud and decrescendo to soft again. This is one of the MOST common long tone exercises. It has been a staple for years and years. If your lips hurt when playing loud be concerned; if they don't hurt when playing loud don't worry about it too much. Always try to some warm downs after playing.

Regarding your opinion of how loud you are playing; you must trust the conductor. Remember your bell is facing the other direction and everybody else is playing directly towards into the directors face.

Now the pedantic semantics on loud versus projecting.. . . . .
Loud is loud and will not necessarily carry to the back of the auditorium. Projecting can actually be quieter than others but carry better because the cleaner and purer sound will cut through and penetrate easier (without being louder).