Yes, 3/16 is what I would shoot for thick 3 to 4 thick,(depending on poundage) and maybe a power lam in there somewhere, I generally can get away from the power lam, but everything better be just right.....but how is the ring count?? That can determine your width along with poundage requirements. After glue up you should be able to tiller right through the lams as if they were growth rings. Pick the cleanist wood you have.
With a one inch thick board, you could also slice it in half and use it as a belly wood without all the lams, using maybe a contrasting core lam.