Here's another new idea, might be a bit off the wall tho! You have an apparent contradiction, that the bikes measure very similar especially after setup, but they feel different and you want to eliminate sizing and setup.
Two odd possibilities ocme to mind:
1. the small differences in dimension are big enough to make the difference you feel, so perhaps you need to somehow match the bike contact point settings better, if you can.
2. The measurements you have taken might be wrong, and should be double checked, or checked by a different method. I'd suggest measuring saddle, handlebar, and BB height to ground making extra sure all vertical measurements are perpendicular to the ground, the crank lengths, the saddle setback relative to BB with a plumb line of course, and the distances from the saddle horn to each brake lever. Millimeter accuracy should be used, since you want to establish what differences are really there. Also you should measure each several times, recording all the numbers and use the average values.
Sometimes when I get this obsessive I can find differences I never noticed before. When I matched two bikes this way once, I got very similar-feeling ride positions. bikes were still different, but my positions were the same.
If you get truly confident that the positions are the same, maybe the other differences between the frames are causing the problem. I couldn't say why, but I would think that conclusion could be the answer.
final thought: if the saddles are really the same, there should be no issue with swapping them between bikes and setting them to the same positions. This would tell you if one of them is more worn than the other, causing some sensation that makes you want to squirm.
Good luck!
Road Fan