I like your idea and want to entertain some thoughts about this layout.
Sound.
Stingray HH has 5-way switch which gives you individual humbuckers, both humbuckers and two in-between positions (inner coils or outer coils of both pickups). Let's see how moving two pickups together affects these options:
View attachment 4326293
Position 5: neck pickup in P-location. It won't sound like Precision because it's not split coil and MM preamp has its own character, but position is pretty much the same, so it may be some interesting new take on Precision sound. In any case, it reduces neck pickup woofiness as you suggest in OP.
Position 4: Inner coils. In this version they're so close together that you basically get another humbucker option! It's like virtual humbucker that's located in "in-between" position. It's like moving your bridge humbucker slightly towards the neck (or heck humbucker slightly towards the bridge). So this instrument basically has three humbucker positions which allows you to fine-tune sound balance between low-end/woofiness and brightness/cutting.
Position 3: Two humbuckers together. Since they're right next to each other, I guess this should give some kind of Warwick $$ vibe (and the pickup placement looks pretty similar to $$).
Position 2: Outer coils. Judging from your original picture this should do pretty good jazz bass approximation.
Position 1: Classic MM sweet-spot bridge humbucker tone.
Looks like interesting set of options.
Design/Visual part
I personally like how two humbuckers look when located right next to each other. It's like one huge mega-pickup. Looks brutal in a good way.
Playability/Feel.
Pickup getting in the way of slapping/popping was already discussed. I'm not a slapper, so I don't know about this. But I like what this layout does to thumbrests. Instead of one comfy place to put your thumb (like on H Stingrays) or two places (on HH stringrays) we get three similar thumbrests. I like the idea of having these options: you can really choose where to pluck.
View attachment 4326300