Randy, are both circuits going to the same panel? If they are going to the same panel then they both have the same grounding. Then there should not be an issue with the 350 being on a separate breaker. If your breakers are in 2 separate panels then you could have a ground loop due to each panel possibly having a different ground.
If both breakers are in the same panel, i can almost guarantee you that the components being on different breakers is not the issue, provided that everything in the panel has tight connections if anything verify your connections are tight.
Due to the amps that axiom use not having a separate ground plug, this could be an issue.
I would tell you, to get an extension cord to run all of your equipment off of one breaker. Plug the Sub's in and go component by component, until you can isolate which piece of gear is the cause of the ground loop.
if you have the capabilities you might want to think of going to a balanced cable system. The RCA's could be picking up some noise from somewhere also....
Hope this helps.
