Recently, my '68 Fury has developed an issue with stalling. I'll start it up and it'll run fine for a while, but if it idles under load for too long (like at a traffic light), it'll suddenly start bogging and die, usually the instant the light turns green. Which is particularly scary if it happens in a through-lane on a four-lane divided highway with a 45mph speed limit, like it did today. Usually it'll fire up again nice and quick, and then hesitate a little on acceleration, but today it took like five minutes to get it restarted. That's an awfully long time to be sitting in a travel lane, especially when your flashers don't work (I popped the trunk, hoping that would clue people in to go around).
So obviously something needs to be fixed here. My first thought was that the carb needs to be gone through. 202,800 miles on the car and I've never been into the carb in the 20 years/30,500 miles I've owned it. But it also occurs to me that the MP electronic ignition (orange box mounted well away from the engine) has been on there for over 17 years and maybe it's time for a new cap and rotor.

Any ideas, preferably not involving replacing the ignition setup that worked fine until a month ago (I'm anticipating the "throw out that crap and get an MSD" replies)?

I'd take out the idle mixture screws and shoot a 3 second blast of starting fluid way into each port with the thin red straw. You might pull the carb top & check the bowl for debris (what carb) & flush it out good. EDIT you might let idle in your driveway in drive/ebrake on & see if it'll act up & have a helper crank it IMMEDIATELY & you under the hood check the coil wire 1/4 from ground for a good blue spark