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The easy way to get those areas even is to add a fingerboard to raise the playing surface up to the top of the box. That way, the part you are gluing is the original planed surface of the board you make your neck from. You can scoop out between them to let the top vibrate - that of course, is a less critical tolerance. Unless your box is all wood (vs. paper covered) and has a fairly stiff top, you should also let the carry-through support the top right under the bridge.
If you don't want to use an added fingerboard, make a flat area to go in the box (with no extra relief for vibration). Get it flat and matching your box top... and then cut the vibration relief. That way the top supports will line up.
Unfortunately, both of these solutions may require starting over with your neck.
Yes, a thick glue will cover the discrepancies. I use liquid hide glue and it will work.
5x3 cm seems a little big (or is that the whole area of both attach points?). Anyway, you don't need much. Just enough for a screw (if you want it) and some glue. In your basic neck-through design, there's very little stress on those joints so you don't need much surface. But do support under the bridge.