I agree with Frankie that the only real solution is going to be a neck reset. Hopefully you can successfully steam it apart.
If you used Titebond Wood Glue, it should be doable, but if you use a PVA it may still be workable but harder to break the bond.

That gap you have there (whilst is should not be there) may turn out to be a blessing in this case.
Once you get the neck removed, I suggest you read through these two recent build diaries that have required shimming to fix the exact issue you're experiencing with yours.

This first LINK is a excellent post by Simon Barden that details making a shim.

These other two links are for the builders' diaries beginning from their post #1. You can work through each to find the relevant discussions about neck break angle etc.

mrpearson - First Build - PSH-1

vivek_rc - PSH-1 Build