If your 4/4 blank was S2S and is now milled true and doesn't deviate much after resawing and smoothing you should end up with material about 5/16" thick. This medicine cabinet insert is 5/16" mahogany and has done fine in the guest bath. the rails and molding act as structural items as well as decorative and the joints are sliding dovetails which makes more delicate structures pretty rigid. If you are lean on purple heart, have you considered using a substrate, resawing the purple heart and veneering the piece?
Any sufficiently advanced technology is indistinguishable from magic.
- Arthur C. Clarke