In my post earlier today I noted that Pocketwizards aren’t always reliable when they have a wire plugged into them. That, and you need to keep them away from 430EX flashes, and point the antenna on the receiving side the same way as that on the sender, ideally.
The “a cable plugged in makes the receiver unreliable” phenomenon is presumably due to some of the RF going into that wire. So a possible solution should have been obvious to a radio amateur/electrical engineer like me:
Yes, that’s is: the little RF choke I put on the cable. And indeed, my testing shows that this type of choke seems to keep the receiver significantly more sensitive. Problem solved (or at least, problem alleviated: the other recommendations still stand).