Aren't you wearing 3A anyway? While not official, that should serve as a functionally acceptable backer for the Tyr plates.
If you can do BALCS, I'd offer (or threaten) to do some things you wouldn't want anyone else to find out about to obtain one of SKD's LVBCs in white.
I had a suit on so lots of layers and noise in front, but I think I could have had at least a front plate without anyone noticing. I try not to talk out of my ass too much, but they're stupidly comfortable and actually conceal better than the concealment vest I had which was sent back multiple times for refitting.
I believe it was Longeye who suggested the concept. Seems good.