All good, sorry for the confusion.
New points 2000 miles ago fixed the double image, which doesn't seem possible. But they did, and now they're rather pitted, and weird timing things are showing up, so I'm hoping the new ones and condenser I just ordered will fix it again, and hopefully the stumbling as well. If they do, I'll add a booster box so they don't pit, and if they don't, I'll try an electronic ignition.
Here's how I think it stands, in order of likeliness in solving the stumbling issue:
1. Bad points and/or condenser causing misfires/dual image.
2. Carbs need rebuilding
3. Bad spark plug wires
4. Bad coil(s)
5. Clogged petcocks
6. Clogged gas tank vent (only putting this last because I'm fairly certain it has stumbled while I had the gas cap loose)
I'm going to go through each one at a time to pinpoint the issue. Anyone have other things to add to the list? Floats seem good, set to be parallel to the base of the carb when the valve closes. No surging before cut out indicating a lean condition. I could set them by checking the fuel level in the bowl, but doesn't that depend on how much is in your fuel lines, as a fair bit dribbles out when removing the bowl?