You may not have any problem other than the float bowls being dry. A lean air / fuel mixture can cause an engine to back fire through the intake. (A rich mixture will be through the exhaust.) With the float bowl being dry, the mixture is likely to be lean while the float bowl is filling.

If it was my car, I would very carefully check out the ignition system to make certain there is not an ignition problem as well. It is entirely possible the car has two problems. Gasoline burning inside the carburetor is not good!!

The only vent on a AVS that I know of is the one that is on the driver's side. It is fairly easy to add fuel to that side, but how do you add fuel to the passenger side bowl? Can it be done?

The holes right next to the metering covers.
Doug

Back in the 70's & 80's, the only carbs that would go dry after just a few days were GM Rochesters in my experience. You could only start GTO's after priming the carbs - it was maddening. NEVER had a Mopar with an AFB, AVS, or Thermoquad go dry - even after sitting for a month. My '71 Hemi Charger could sit all winter & it would fire in the spring after pulling the choke, a few pumps to the floor & a little cranking.

The Rochester's had the same problem as the TQ's,leaking wells under main jets.

Doug, Is this the spot to fill the passenger side bowl?

Check the underside of the AVS for main well plug leak. Too much time in the carburetor dip can damage the aluminum main well plug on the bottom allowing the fuel to drip out/into the manifold. If it's difficult to drive when cold then there's a miss-adjustment on the choke valve or the thermal bimetallic choke thermostat rod on the passenger side (pictured).

I'm pretty sure the factory correct carburetor base gasket will cover up the main well, but I'm not sure. Old age memory.

A stuck exhaust manifold flap valve (I forget the correct title) located in the passenger side manifold can cause the intake manifold to run too hot and boil the fuel. Make sure the spring loaded valve can open fully and move freely.

BTW, I too have a 1969 RR 383 with a 4615 AVS. Best of luck and we need more pics.