I have a similar problem with a JTV-89F but with the "A" string - I thought I had the problem resolved but it's back again.
I have noticed that if I have the guitar plugged into an amp without turning on the modeling all the strings are even / balanced. As soon as I turn on the modeling the "A" string has less output/volume. All the others remain as they should. I've checked all the global volume settings and everything is set to 100%.
Did you ever figure out what was causing this for you?