A quadrajet is a great carb IMO and can be rebuilt and tuned pretty easily. My qjet was doing the same thing after sitting for six monthes, the float needle wasn't seating right and I took it apart one day and cleaned it out and put it back together and then it was as good as new (it actually was pretty new as it turned out according to the reman date sticker on the side of it). I like quadrajet carbs and I think they work pretty well when functioning correctly. Backfiring through the intake can damage some carburetors. My 350 will backfire through the carb sometimes when I stomp the gas pedal at idle if the ignition advance is set too retarded. I learned this because I sometimes back the timing down (sometimes too much) when pulling the trailer at high speeds on a road trip. It (retarding the spark advance) makes the motor feel more relaxed at 90 mph and I like to go fast. Hope I didn't confuse you, I didn't mean to. See what vacuum line goes to the distributor, I like the vacuum line that only pulls vacuum when you hit the gas. Some people use manifold vacuum.
I am sure somebody can word this better than me but you need a timing light and a piece of chalk.