I'm remembering the evening in about '67 or '68 when I ran my old '60 Chevy 2dr HT out of gas on the way home, and bummed a couple of gallons from the farmer near by, out of his storage tank. Got it lit off, but it ran like crap, popping and cracking, backfiring through the carb, and generally being a PITB trying to get the five miles to town. Limped into a local shop, and the guy pulled the 4 bbl carb off of the old 348, and dropped it into a 5 gallon can of Gunk carb cleaner. The next morning I was down there early and he took it all apart, and put in the kit, spending a bit of time getting the float level just right. An hour later the carb was back on the car, it lit off after a bit of cranking to get the float bowl filled, and ten minutes later the idle mixture was set and I was on the road.

I'd concentrate on getting the carbs cleaned up, back together, and back in place before I chased any more rabbit trails other than tracing and maybe replacing vacuum lines if they're old and dry. Running out of gas generally doesn't result in a bunch of other problems. Chase one gremlin at a time would be my recommendation.