I have figured out the sound imbalance issue! Stick with me, because this is a peculiar finding. As I was switching around the tips to find the best fit, I noticed something different between the right and left tip. Take a look at the attached picture. The hole in the tip on the right looks white, while the hole in the tip on the left is clear. On close inspection, the white in the tip on the right is caused by a thin piece of what looks like cardboard. To the right of the tips is the small obstruction that was removed from one of the other tips. After removing the obstruction, the tips now work perfectly, with sound centered between the ears as it should be. Now, finding this obstruction in the tip is peculiar. Where did it come from? My theory is that the obstruction came from the small case that housed the two spare tips, pictured on the right. When I first accessed the spare tips, they were firmly attached to the case. I suspect that there was a small cardboard disk that was holding the tips in place, and that the small disk tore off and remained inside the tip when it was removed. This theory is supported by the fact that the spare tips no longer snap into the case, suggesting that something has happened to the spot where they are anchored.
When I tried the large tips, the sound from the Airpods was completely muffled. Upon inspection, both tips had the embedded piece of cardboard. When removed, the tips work perfectly.
I think this is faulty packaging, and will be reporting this to Apple. I can't be the only Airpod Pro user who will encounter this issue.
And to answer your question, the ANC worked pretty good during my fitness center visit.