how could the clumps be getting through the second filter?
There are several places that will allow crap to fall directly into the fuel bowl area of a Q-Jet carb, including the 2'ndary rod holes and that big-A vent.
There's a good chance the junk is coming from the filter assemble somewhere- and if there's been a rat under the hood- it might really be
Take a good, long look at the air filter assembly for any small leaks where crud can get past the air filter (you ARE running a filter, right?) from inside the filter housing (including the carb/air cleaner base joint- it needs to have a paper gasket to seal the air filter base to the carb).
Has the car- since you've been driving it- ever
run right? If so, what has been changed AFA the timing or carb settings?
Does it start easily? Does it have a clean, non-smoky exhaust?
Does the engine miss, or is it "smooth, but slow"?
Hate to ask, but you're sure it's a Pontiac and not an Olds 403, right? IIRC, if it has a Pontiac, the shaker will say "T/A 6.6". If it's an Olds, it'll say "6.6 Litre". The Olds will have 10 bolts for each valve cover and the oil fill tube comes out above the water pump.