Couple of simple things - perhaps the tweeter on the right side is revealing the effect of reflections from surfaces around the right speaker that are not like the room reflections from the speaker on the left side. The first thing I would do is to simply reverse channels at the amp and see if your highs still shift to the right.
Is your listening position equal distance from each speaker and are you sitting dead center? If not carefully create that condition and see what happens.
You don't mention your electronic's but if you have tubes try reversing channels to insure that you don't have a 'hot' tube on the right side.
If all that is of no effect, time to carefully revisit TT set up issues, VTA, VTF, as well as anti-skate.
Hope that helps a bit.
Is your listening position equal distance from each speaker and are you sitting dead center? If not carefully create that condition and see what happens.
You don't mention your electronic's but if you have tubes try reversing channels to insure that you don't have a 'hot' tube on the right side.
If all that is of no effect, time to carefully revisit TT set up issues, VTA, VTF, as well as anti-skate.
Hope that helps a bit.