You are going to have movement issues at the transition from wood framing to slab. The way to prevent movement would be to have a 3/4" plywood underlayment span from framing to slab. So you are going to have to raise the whole thing by 3/4" which is going to mean transitions in height at all other entry points.
The plywood can be attached to the slab (after moisture-proofing) with glue and con-sert (tapcon) screws.