You are sure the tap you found is M10 x 1.0 mm, not the much more common M10 x 1.5 mm right?
Dropouts are typically 5 or 6 mm thick and sometimes a bit thinner on steel frames For quick release hubs you want them thick enough to be sure the axle stubs don't stickout beyond the outer face and prevent the qr from clamping the dropout itself. Since axle protrusion is generally 5.5 mm per side, that's a good minimum thickness.
However, your 3/8" plate is 9.5 mm and 5/16" is 8 mm so both are muchthicker then that. 1/4" plate is 6.4 mm and closer to commercial dropout thickness and should be sufficient even in aluminum.