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I'd say there was plenty of meat there to play with. So, the original threads are only 3/16" deep? that doesn't seem like a lot.
If the threads are in good shape, and match the depth of the new head, I'd be tempted to loctite the heck out of the new replacement and call it good.
When in doubt, take the easy way....if you lose the new head in a few 100 miles of driving, then you can take drastic measures to drill, tap, helicoil, cuss, bleed, drink, break bits, bleed some more, cuss, etc
Bobby