Thanks for providing the video; that certainly makes the problem a lot clearer. You've certainly got some serious interference there.
It sounds to me like the signals from the radio tower are simply so powerful that they're overpowering all the shielding and pushing interference into the signal path; so much so that some audio components are squeezing in there. Almost certainly this is because you're so close -- signal strength falls off with the square of the distance, so even moving a short distance away would probably yield a huge improvement.
Part of the problem is that you're using a 3.5mm-based system. 3.5mm uses unbalanced connections, which have basically no protection against interference. Shielded cables help, but can't provide complete protection, as you're hearing. A balanced system -- which generally uses XLR connectors -- would help a lot; but your camera doesn't have XLR inputs, so that doesn't help much.
(BTW if you want to know about connections, I made a video about that: https://moonblink.info/FieldRecording/content/course#Connections It says "field recording", but the same connection types apply.)
Unfortunately I don't have much to offer you, and in your situation, I can't think of a way out that doesn't involve spending money. For example, an XLR mic going via XLR cable into an external sound recorder might get you clean sound. But I wouldn't know, except to try it and see.
A camera with XLR inputs might help, but that would be really expensive. C70 for example.
Just shortening the signal path as much as you can would help -- at least a bit. Use shorter cables, and maybe if you have any kind of audio recorder, just put it really close to the mic with a really short cable. Good screened cables would help a bit too, but maybe not as much as you'd like.
Hopefully you can experiment a bit and get past this, 'cos your video looks pretty good. Best of luck.
