Others have already implied it, but azimuth adjustment has very little effect on channel balance, as you already have learned by direct experience. And the goal of azimuth adjustment is to minimize crosstalk, not to balance the channels. I was interested to read that Larryi says intrinsic channel imbalance of a cartridge is often more than 2 db. On the other hand, there is a prominent poster on VA who says that if a cartridge output is more than 1 db different, R vs L, that cartridge is defective and should be returned to the seller. I have no idea where truth lies on that spectrum.
One thing you might do is to swap tubes in your phono stage, R to L and L to R, and see what happens to the channel imbalance. It is possible that your entire problem is due to a difference in gain between the input tube on one channel vs the other; that's where most of phono gain is achieved.
One thing you might do is to swap tubes in your phono stage, R to L and L to R, and see what happens to the channel imbalance. It is possible that your entire problem is due to a difference in gain between the input tube on one channel vs the other; that's where most of phono gain is achieved.