Matthew,
Here is an idea: Use 1/8" thick bass stock. Make (file, hacksaw...) 3 or 4 1/16" deep dovetail grooves across the insert. Fill them with epoxy (J-B Weld?) then attach the insert to the sole. You could also (additionally) score a 1/16" deep kerf (it does not have to be dovetail shape) across the insert, also filled with epoxy before attaching.
Best wishes,
Metod