It's going to be hard to get a neck with that big a heel block and lots of glue contact with the sides and bottom out.
The luthier way to do it would probably be to take a couple of frets off towards the front and rear section of the heel join area, drill holes down at the bottom of the removes fret slots very near the sides of the neck, and then inject steam through a hypodermic needle tip into the holes, putting in moisture but more importantly, heat. Once you've prised the neck off, you can replace the frets.
You may be able to do it with heat alone, using a couple of hot air guns blowing at the guitar for quite some time. You need to allow time for the whole guitar to warm up. It probably won't do wonders for the finish.
If you have any visible cracks at join areas, you may be able to slide in some heated thin spatulas (I bought some painters spatulas in case I had to do this as they are very thin, but probably don't have enough heat capacity to work well unless heated up very hot). keep inserting and working at the glue a little at a time.
Otherwise you need to work with what you've got. Can you post a photo of the height under a straight edge run along the neck?
You may be able to use just the top of your Amazon bridge, so it's sitting directly on the top. Once you've located it correctly, you could pin it and drill a hole for the piezo cable.
If you've got a bit more height than just enough, you might be able to drill holes for the bridge posts directly into the top, and fit the top part of the bridge on that (a bit like a Gibson ABR-1 TOM on a LP). I'd suggest gluing the posts in once you've worked out the correct height for them, as the bridge block wood will be very soft.