I was wondering if it could be due to some combination of the vent orifices or hoses, and the fact that it's on the 2 line petcock. because the burps are coming from the 3 & 4 carbs which are on the same fuel line. So maybe it could be that air in lines or vapor lock could be holding fuel back, and then pressure is equalizing suddenly and allowing some gas to come through before floats react?
Dirt in carb is certainly possible but I've been in there a few times recently and I don't think it's the case, unless it's inside one of the internal passages (has happened to be before on a 350).