So in the Line 6 forum I came across a guy who was getting differing tones depending on how he set up his patch for things that should have had no impact on the tone. I tested 3 of his claims, listed below. The links link to mp3 files of my tests.
I could not find the tonal differences he perceived, and it turned out he had a corrupt firmware. After reinstalling his firmware, he was not getting the tonal differences for the things listed above.