What is the cause of the slanting arc as I pan? Is it parallax ...? Or is it that I'm not doing a good enough job leveling the tripod?
It isn't parallax.
If you're consistently getting a similar upwards "U", then the consistency means you are doing a good enough job leveling the tripod (or at least trying to), but that that you're being lied to by your tools. The upward "U" shape indicates that the bubble level on top of your tripod (or at the base of the ballhead) is not actually level. Essentially, when your tripod tells you level, the base of the tripod is aimed slightly foward. While this is compensated for another, probably truer, level with the camera on top of the ballhead, realize that the axis of rotation of the ballhead's panning base is still tilted slightly forward.
Here's a simple experiment to demonstrate what I'm talking about, without involving any equipment. Tilt your head forward at an angle, say 30°. Most of your field of view is below the horizon, even if you look up to the horizon with your eyes (keeping your neck tilted). Now rotate your head left. Notice how the amount of sky / above horizon in your field of view increases. Same if you rotate your head right.
I'd really like to be able to pan without constantly adjusting the ball head in each stitch position.
Assuming you're only doing single-row panos (where all shots are parallel to the horizon, you're not taking a row of shots aimed up or down), there are a few solutions available for you. In order of increasing cost:
Get a supplemental level plate to put in between the tripod and ballhead. This is probably the cheapest option
Get a panning base to put on top of the ballhead:
Without changing any other gear, the 2nd option will improve your horizontal panoramic stitching much more than the first. Why? Because you don't need to worry about leveling your tripod anymore. Your ballhead becomes the sole point of control for level.
Think about propagating errors for a moment: to get an absolute level panning base in your current setup:
- You have to trust the tripod's level (which appears to be untrustworthy);
- Be able to level the tripod (which is always at least slightly frustrating);
- Trust the ballhead's level;
- Be able to level the ballhead.
But with a panning base on top of the ballhead, you only need to:
- Be able to trust the panning base's level;
- Be able to level the ballhead.
All small commodity bubble levels are quite low precision, and if they aren't installed correctly, then they aren't worth anything. So eliminating one possibly-questionable "sensor" from the process is a big win. And even if all your bubble levels are good, and mounted well, reducing the necessary points of control is also a big win for accuracy, repeatability, and setup speed.
A leveling base plus panning base on top can eliminate your need for the ballhead ((assuming you don't need any other features for a ballhead, such as the 90° horizontal drop notch, or mounting the camera non-level for artistic reasons).
Both of these leveling bases perform the same function, to provide a level base for whatever is on top of it. The first, a screw-type leveling base, levels just like a tripod, just with way more precision and substantially less fidgetiness. The second, a bowl-type (or mini-bowl) leveling base, levels similar to a ballhead, with a single control point but multiple degrees of limited motion.
Without any other equipment on top of the tripod, however, this setup is limited to horizontal shooting only. Instead of a panning base on top of the leveling base, you could use a pan-tilt head, which is functionally equivalent to a video head in terms of rotation axes):
Personally, this is my preferred route, because it specifically eliminates the roll-axis degree of freedom, meaning that when aiming the camera, a single control knob controls only a single degree of freedom. These types of heads tend to be lighter than ballheads for equal amounts of load carrying capacity and stability provided.
At this point, we're getting into replacing the tripod with one that can accommodate a leveling bowl or video bowl, with a video head or pan-tilt head. But these are just heavier-duty (and correspondingly more expensive) variations of the previous point.
If you need to orient your camera in portrait mode (which is my recommended orientation for landscape panoramas), an L-bracket provides faster, less fidgety, and more repeatable setups than using the 90° drop notch that most ballheads provide. The drop notch of many cheap (and usually small) ballheads is not precisely 90° with respect to the panning axis of the ballhead, so once you get the ballhead base level, tilting the camera sideways into the ballhead notch is another exercise in fidgeting: holding the camera in 90° orientation (a few small degrees above the bottom of the notch), as well as aiming the camera at the horizon. Finally, once the level is found and the ballhead is locked down, when you let go of the camera, the off-axis weight of the camera and lens causes a tiny bit of relaxation or sag by a small amount, requiring more fidgety adjustment.
This is (mostly) avoided by using an L-bracket on the camera to keep the weight above the rotation axis.