Would I be best served adding the isolator to the feed in the basement or just at the location where the problem is? It's functionally the same at the moment since we're only using one coax drop, but still...
Looking at the web page of the isolator device, I notice that it's a female-female device, meaning that you're going to need a short section of male-male patch cable to connect it up, as
illustrated. So I'll bet that's going to be easiest at the cable box itself.
Also, if that works, I'm wondering if you should just be fixing the cable grounding problem instead of using an isolator. For instance, where my cable drop comes into the house, there's a ground wire connecting it to an exterior pipe that goes into the ground. Maybe that's all you'd need.