Oh, hello! FtM lacrosse player here.

I totally get your point, I was mulling over it this afternoon.
Honestly I was in the mood of "I prefer to get hurt rather than having to deal with those things" but then I realised that it would help the whole passing thing. For your reference, I would do without bras for life, so this is my starting point.
I was thinking first to use my regular contraptions, bras designed for ballet dancers that are skin coloured, with no underwire or padding, ultra-thin straps, minimum of cloth: less than that there is only body painting. I hoped to hide the whole thing beneath the chest protections the whole team use anyway (and isn't it warrior-like and gorgeous?

).
However... yes, the whole passing thing. I considered using the things I used in martial arts, but they have rigid breast-shaped cups and there is too much Xena warrior princess in it, I always hated it dearly.
I want to figure out if a compression bra or a very strong sport bra, provided they are not too girly. Still looking/hoping for something skin coloured. Totally stay away from binding and also those bras one size smaller than yours, you need to breath really hard.