It's still a net loss of 16 Piety with the loss of a bracelet, which, considering that I'm still under cap, will be a painful loss.

To compensate, I'd have to sacrifice a STR ring, so yes, the result is a loss in STR. About 10 STR to be exact. Doing it without the coat results in a Piety gain for a loss of about 2 STR. It's the Critical Attak Power I'll miss.