Noah,
I'm not a mathematician either nor do I play one on TV so the actual math eludes me. But I do know something of the mechanics involved based on experience. A roller sheave and line works best when pulling from dead center, however depending on the size of the sheave, line, application and installation there is an off center radius of operation of a certain number of degrees where the rig will still perform well. I don't know if my dinghy raising evolution is within that envelope but if not it's got to be pretty darn close and that's just based on actual experience.
FYI, a couple of years ago I replaced the main halyard for safety reasons since it's how I get up the mast. I examined the old one to see if there was any reason for concern other than peace of mind. Other than being faded I found no signs of chaffing or other damage of any kind. This is just my experience, I like to keep things as quick and simple as possible, as you say Your Boat, Your Choice.
BTW, in the thirty-four years I've owned my boat I've had two jib failures, both were the sail, not saying it doesn't happen but I've never had a busted halyard, jib or main.
Ron,
When my dinghy is in the water for a week or more I find 5min with a mask and a scratchpad once a week remedies that problem. It beats having to pull your dinghy out of the water every night.