The Axe FX II has the highest/strongest output signal of any device I have ever used. Try turning down the GLOBAL 1 output EQ's output volume. It looks like a graphic EQ with a bunch of frequencies, but the last slider on the far right is an overall volume. Try lowering that slider to -6db to give yourself some better control on the rotary knob on the front panel for output 1.
You can also look at the output on a meter by pressing the utility button on the front panel and then page right 1 or 2 times. You'll see the input level and output level. If your output level is slamming the highest peak of the meter, that is where you're hearing digital clipping. My suggestion of turning down the output 1 at the Global location should help elevate the problem.
Depending on how you shunt between effects and even empty blocks that are running in parallel to your main audio path in your preset, you can have tremendous boosts in gain. The sky's the limit in routing. That's why it is awesome that the amp block output has such a wide operating range. You can cut the amp output back and check your progress on the utility gain meter screen, to make sure your output is very close to matching the input of your guitar.