I've had that much play in the neck pocket of MIA Fenders with original necks, so it isn't necessarily a problem. If you line up the screw holes without needing to force it, you shouldn't damage anything. Get the screws in without forcing it. Put the strings back on with just enough tension to make them straight, loosen the neck screws a bit, gently align the neck and re-tighten the screws. I like to use a business card or two to help keep the neck straight while re-tightening and then remove them.
I would be surprised if you notice a significant difference in resonance, but you can always put the original neck back on.
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