I know it's going to be a pain to sand it back and start over, but there probably aren't many more LP kits like this out there, and this guitar has too much potential not to give it another go
Once you've got it sanded back you could always stain it black instead of painting it; that way you wouldn't have to worry about swelling. I did the back and sides of my LP with stain and it's none more black
I really like your headstock shape and hardware choices. I know you'll get this sorted out and I'm excited to see what you do with it!