In the realm of goofy tire problems, might I suggest that you carefully check the rim tape and wheel for burrs? I had a wheel that drove me crazy with metal burr that came loose. Had flats all the time and they seemed to move. Sometimes they would be on the inside part of the tube like a snake bite and sometimes on the outside of the tube. Finally narrowed it down to the burr when it got embedded in the rim tape.
Be careful looking for it. Burrs can be small, sharp and painful!