I've been a lurker for years on TB and it pleases me that we are all working on a handy method to get a solution (or solutions) to this problem. I mean this in the most supportive way.
I'm initially from the big&little ring era. Then the ring and pulley, etc. Due to my locale and the other options available, a leather or conduit friction sleeve is my basic tool. I'd have to look up in Tree Climber's Companion how to set the other systems.
Maybe my contribution here doesn't specifically answer the OP's question. Jon will come to understand simulating the scenario low and slow, when the sun is down or its raining, will answer his questions.
I've observed Mumford's use/promotion of a 5-7mm cord to do an intermediate positioning over trying to manipulate throw line. Makes sense and is economical to have a specific application line for manipulating this specific hardware.
I'm recalling using the pop-bottle-trick, but with a twig, to remotely get a throw line jumped out of the space between the pulley and cheek plate. That's in my bag of tricks, but isn't as profitable timewise, as running a cord that wouldn't ever jump out.
But maybe I could come up with a solution at the $300-500 price point. Y'all would be throwing money at me to get one in your hands.
