The line isolator you describe is a common-mode choke, and will reduce stray shield currents in the coax to the tuner, without affecting the RF signal carried by the coax. It is also called a "balun" (short for "balanced-to-unbalanced").
I like the idea of the isolator, and it should help reduce any RF ground-loops. But, I still think you need a good ground on the
radio. because otherwise you are (by using the isolator) floating the chassis. The 12V power leads may provide an adequate ground, but then again, they may not. If the chassis is floating then you are much more likely to see interactions and
interference from the other
cables that connect to the
radio.
I am still puzzled as to how a line isolator such as yours could cause the problem you have by being defective. It works fine on the lower frequencies, so there aren't any shorts or opens. The only other thing that could be wrong is either an overly-lossy ferrite, or one that isn't permeable enough (a cracked
core could do this). But this shouldn't affect the RF signal, only whatever common-mode signal there is. And it certainly shouldn't make a difference if you are just keying the mic but not transmitting a signal.
If it were my system, I would keep the isolator and ground the radio (as an
experiment, anyway).
It could still be a broken radio, of course.
For what it's worth, I am an ex-engineer, have an advanced ham
license (wb6cxc), and used to design
VHF transceivers. My last job was designing 10 and 40 Gbit/s electrical/optical systems. This doesn't mean I'm correct, but at least I can talk the talk.