wow that does sound bad.. to me seems like a bit of bad AD/DA how do you have your kemper connected? there is not 2 inputs doing the same thing is there? some internal feedback or something?
However here is the bad news..
I had soemthing versy simular as this few years ago with a tele, worked great with some amps.. and others it would do as your clip is.. the guitar was back n forth to the guitar tech and whatever he did the sound problems still were there. - bottom line, I replaced the Pickups and all was Ok.. I agree that this is NOT normal thing to have to do.. but as a test try this..
Load up a rig, Roll the tone down slowly,, does the bad stuff disappear? - If its still noticeable when tone is rolled off completely, then its a dodgy pole piece. - Although in fairness, I DOUBT HIGHLY that it is this, as you have already tried a different guitar.
Try it with headphones.. if it still happens then the input on the kemper might be faulty.
IF it now happens on ANY rig you use then there is defo some fault somewhere..