...I'll put the coax right on the ground to (hopefully) reduce RF.... Thanks in advance. Craig
If you do have RF on the outside shield of the coax, that won't do much to alleviate the situation.
A proper balun at the antenna feedpoint is the first - and proper - step for that kind of problem.
First move the shack, then see if there are any problems for there may not be any. Only cross bridges when a bridge actually appears in front of you, spend little time contemplating on unknown horror possibilities, is my advice at all times.