Couple of things:
a) as someone who only wants to pass some of the time, I regularly strap my chest using very sheer bras one size too small, or tight undershirts....drag kings have been strapping down bigger things than Ive got for a lot longer than i've had 'em!
b) man-boobs are a fact of life for so many people. they don't stick out as much as you might think.
c) weight gain is very important if you don't want boobs. Basically, if you eat a minimal diet, calorie restricted, you don't have much extra fat to redistribute to your chest.
d) or just realize you only get one go around this life. do what makes you happy, and who cares what strangers say?
Either way, give up on the idea of sleeping on your stomach for a few years!