Screw orientation doesn't make any difference at all to the signal polarity. Gibson decided that screws outwards looked best, so that's how they got installed on Gibsons and everyone else with that style of humbucker copied them. The only difference to the signal polarity is made when connecting up the pickups in reverse or the magnet is rotated 180° along its long axis. So you can happily rotate the neck pickup if you want to.
What you will find is that different manufacturers have a different standard output signal polarity, so for example Seymour Duncan pickups have a different output polarity to Iron Gear pickups and you'll have to swap the connections over on one of the pickups if you mix them for the 'both pickups' on position to be fully in phase. Fine with 4-wire pickups but not easy if both single wire pickups (where flipping a magnet on one of them is probably the easiest solution).
Your wiring appears (from what I can see on the photos) to depend on the copper foil providing the ground link to all the pots via the selector switch. I'd look at installing a dedicated ground wire to the pots, which may help with the output issue.
You aren't doing any coil splitting here, but I'd suggest that if you were, the physical position of the selected coil makes more difference than the slug/screw selection. The nearer the bridge the coil, the brighter the sound, the nearer the neck, the bassier it will be. Bit also, screw poles will be physically nearer the strings than the slug poles, if only by a couple of mm, so should have have a slightly stronger output with more low end compared with the pickup rotated and the split coils in the same position.
How different are the pickup outputs and what are the respective pickup heights like? The bridge will often need to be set fairly high, and the neck quite low. It can also be misleading guessing levels when listening to the sound because the extra bass from the neck pickup will always make it seem louder, even though the bridge output signal voltage can be hotter.
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