[quote name='Evil Undead' timestamp='1507454790' post='3385472']
I'm confused - who said my current neck doesn't work properly?
[/quote]
You said in your OP "there's also issues with overtones and deadness on the E string"
So the neck could be warped, poorly attached to the body, tuner in a wrong place, headstock mass may need adjusting, fretwork needs seeing to, or any other adjustment.
Why? Because you ruled out strings and setup thereof and amps etc.
Why the new neck anyway? I'm just curious where the dead E is coming from.