It all comes back to it being much less work to infill the bridge rout and cut a new one than removing and reattaching the wings, so it's about saving the time and work. To be clear, I could totally be wrong, my suggestion is just around accurately assessing the issue so you can proceed in the most efficient and least destructive manner.
I guess I'm wondering if it's a neck alignment-to-the-body issue or a "neck has a gentle arc from nut to butt" issue. Putting a full length straightedge can immediately show which one it is, in a way that a string can't (as a string is not rigid). I'd put a straightedge from the nut down to the saddle line (scale line) and mark it on both sides. Directly in the middle of those marks would be the center of the neck beam and the point over which your strings need to be centered. That will tell you right away if your neck is centered in the body or not.
If it is centered in the body, then the quickest and easiest way to repair would be to infill and reroute the bridge and leave the body/neck joint as-is. This approach is much less work than cutting the wings off and realigning them.
Connected to this is my wondering how the wings could have been misaligned in the first place such that they would throw off the bridge alignment... Because it's a neck through, the beam is automatically 'straight' if it's tapered evenly side to side. You can then glue on wings and move them towards or away from the 'butt' and they can't really impact the alignment. Regardless of where they are, they will end up parallel to the neck beam.
Anyway, I don't mean to talk at cross purposes, I genuinely only wish to help here. In the end, no matter what approach you take, I'm all for it too, as every build, every problem we solve, only serves to increase our skills and knowledge.