This is a very original project you have and the 3605 should indeed be compatible with it.
I personally like the solid case back of the 3738/5738, which I see as a wonderful opportunity for a meaningful engraving (I dream of the 5738/1R with a celebration engraving for my 30th wedding anniversary).
But I totally understand your desire of a see-through case back and wish you all the best for the making of this "bespoke" 3605!
Best, Emmanuel