I suspect that the IC-705 users are using an external tuner that is probably designed for a long wire, like the AH-705 or similar. I suspect that the same thing may be at play with the KX2 tuner.
The problems may disappear if you use an external tuner with a connection for a balanced antenna 
(not helpful I know)
I would try a earth connection to a peg in the ground.
Now on the list to try.
You may still be suffering from altitude sickness following your recent GM visit… you sure the KX2/KX3/TX-500/705/FT-817/8 users were behind you and not ahead of you? 
I’m with you on this one Kevin - Tim, I’d run a wire to a small nail or metal stake in the ground and attach the wire to the case of the X6100 as the next option to try from what you have found. I’m surprised that there does not appear to be an earth screw on the X6100’s case, provided for this. Perhaps you can use one of the screws that the support leg hinges around?
73 Ed.
Worth a try, Tim. For me, 100 nF worked (different rig and mic). And another 100 nF from mic gnd to gnd, if applicable.
Ahoi
Pom