That's why I shoot vertical & use a mild telephoto!even with overlapping it seems to provide a bowel effect when joined together.
I know its counter-intuitive to get panoramas with a tele, but what you're seeing as a "bowl effect" is cause by perspective from wide angle, or to a lesser extent, standard length lenses. As mild tele (about double standard, no more, flattens the perspective slightly making for a flatter transition from edge to center of each image.
Leveling needs to have the tripod legs & head dead horizontal, not just the camera platform. I have a couple of cheap bubble level capsules on the actual top platform below the ball or pan/tilt head for just that reason then a second bubble in the flash shoe lets me get everything dead level before I start.