Yay!
I took off the neck, cleaned out some bumpy paint residue (odd) and filed the holes in the neck (they seemed to have developed a lip of sorts from the drilling).
Put it back together and I was able to lower the tremolo/bridge quite a bit. The tremolo now works without the springs catching on anything. Success!
https://i.imgur.com/1aB9w3Y.jpg
So I finished it up tonight. My son is very happy and so am I.
I doubt we could have gotten a guitar this nice for him for ~$220 (kit plus paint, basically), much less one in the exact colour he wanted, etc.
This is for sure gonna be an addiction. The new offset Tele kit is probably next, hah.
https://i.imgur.com/tbAo5ks.jpg