Smoother bass by running woofer out of phase?

I think you have a difficult room where the bass traps do not suppress its resonant modes adequately. Wiring the woofers out of phase causes their bass sound waves to cancel each other out, resulting in reducing all your bass sound, including the unwanted resonances. I think you would be better off with a room analysis and an equalizer treatment that specifically reduces the resonant frequencies while leaving the nonresonant frequencies alone. There are systems that do this, like Rives, TacT, or even Behringer.

So you've achieved a pleasing speaker coloration. There's a real chance that "correct" bass will not sound as pleasing. If this were the midrange or the highs, I would say that you might become more aware of the coloration as you play more material and you would ultimately become tired of it. This might not be the psychoacoustic conclusion for bass, however. It's an intellectual choice, pleasing coloration or accuracy.