Hey Sean!
The old man (Roy from PA) builds a fair number of these and may have some more advice but I'll throw in my two cents.
Better to have a little extra meat on the belly, so I would probably make the core 3/16 tapering to 1/16. Maybe you could go thicker, like 1/4" tapering to 1/8", but obviously you'll end up with a thinner belly slat after tillering.
Search through Roy's threads, he's done at least one buildalong and probably answered this question 100 times.