I've reached the assembly stage on an Es12q

The neck angle is not good. I thought I checked it well enough before gluing it in, but it seem not. I'm looking at about 3.25mm at the 12th fret with the bridge cranked all the way down and the neck dead flat. The nut is still a bit high, so there could be some improvement in that area. There's not a lot of room to take it down further at the bridge, because then the strings would be too close to the pickups.

Has anyone had any experience steaming off this sort of neck? Any suggestions on how to go about it?