Haha, thanks for all the great advice, especially from the "wash your shirt if it reeks" contingent!
Intuitively and just from initial experience I am with neph93 in that I find rotation btw UHF shirts and giving them plenty of opportunity to air out can extend the "reekless" lifespan by quite a bit.
Thanks also to Maxpower for the recommendation to stick to hand wash to retain the original look. Will definitely keep that in mind.
Cheers