"Full Head Job" should have included cleaning up the threads while it was out and readily accessible.
I'd use a chase, not a tap, at least at first. Most auto parts stores will have them. Also, I'd get a mirror down in there and see what's going on. If you have access to a borescope, that would be better.
If you tried forcing it even slightly with a wrench, you could have crossthreaded the plug and getting that straightened out with the manifold on is gonna be a real pita.
if you have access to a lathe, I'd take a plug, turn the first few threads off real close to the minor diameter, use that new diameter as a pilot in the hole, and then start over. You'd also have to manually remove one thread then to first make sure it would start in a new hole with no troubles. The lathe will roll back one thread and of course that won't work. You might have to tap a dummy piece of aluminum or something to test with before going into the head.
With no hope of fixing it on the car if the tap starts cooked, I'd be skeptical about trying to reform threads that way. What might work, though I've never tried this, would be a rollform tap. At least it won't remove material. They're not intended for deep holes, and not intended for hand use, but it might be good enough to get you started, which is all you want.
Anti-Sieze paste should go on these things all the time anyhow. Never assemble aluminum parts without it. I just rebuilt my engine and every single hole was chased and pasted. Every one.