You should only have needed to move the neck away from the bridge slightly, just enough to get the edge of the pickup ring resting on it so there wasn't a visible gap with the cavity not showing. If you do that, then you can happily intonate the guitar - at least my EX-1 did.

Sometimes the cut-outs for the pickup mounting 'ears' aren't big enough to allow the pickup to move much. I've often had to enlarge these a bit. I find a Dremel with a sanding drum bit works well for this. As long as you remove within the outline of the pickup ring and leave enough wood for the ring mounting screws to bite into, you can remove what you need to.

As you haven't got any finish on, then steaming could be an option, especially as the neck join area isn't particularly large. But this is only possible if you've used PVA or Titebond original (which is also the stuff Pitt Bull sell) or hide glue. Anything that's waterproof or has a higher melting point and it won't work.

The standard method is to inject steam into the joins using hollow needles, but this is generally used to preserve the finish as much as possible. So steaming the whole neck area can work, using a kettle or saucepan (but wear suitable gloves to avoid scalding yourself, preferably rubber over something more insulating). You'll need to take the lid off most kettles top stop the pressure switch from cutting off the power once it boils. Or you can try inserting a thin heated pallet knife into the joints (or a combination of both). Light pressure only when trying to prise the neck away from the body. When the glue's lose or melted enough, it will come away easily. Otherwise the glue joint is stronger than the wood, so too much force with intact glue and you'll tear out bits of wood. Once things start to move, the steam will penetrate the joins more easily.

But if you do this, then let the wood dry out thoroughly before re-gluing. It will swell up considerably, so it needs to be dry before everything fits. And check with the pickup in-situ that the chosen neck position allows the pickup to sit freely in the pickup rout.

Otherwise you can pick one of FrankenWashie's suggestions.

As you are doing a solid colour, then any marks you make can be easily filled in.