I don't think the headstock angle would make a difference, but it shows that the nut pocket is shallower on at least one version.
I guess I'd try to put a shim of some kind under the shorter nut, if it doesn't raise it too high for the screw holes up line up. I'd try making out of the harder scrap wood I have around.
Or I'd look for another nut. That's probably the simplest. I see 4 on eBay right now, for $11-13. If you want to be sure, you could message the sellers and ask the exact measurements. A good seller would reply.