'84 K10 Sub: Gas dripping from Exhaust

[93w/t1500]

My poor '84 Suburban (350, Q-jet, SM465, non CCC) has been experiencing some horrible drivability problems. In fact I had to tow her back to the house yesterday. Starting a few months ago I had a problem where she would hesitiate going uphill and then stabilize once the load came off the engine. That progressed to stalling fits when the engine was under load and finally stalling whenever I gave her more than 1/4 throttle. As far as I could tell the engine was flooding out so I pulled the Quadrajet and rebuilt it this weekend. I put it back on the truck and she started fine so I went for a test drive.
She ran fine for about 5 minutes and then started stalling again. The difference was that it wouldn't clear up once restarted. If I held the throttle nearly floored I could keep her running roughly at about 1100 RPM or so but she would die whenever I tried to let the clutch out. The truck was definately running rich again...in fact the cat was glowing cherry red and the undercoating was starting to cook off the underbody.
I got her home, pulled the Quadrajet and checked it over again. Everything seems to be ok but I didn't get metering rods and jets in the rebuild kit. I started her in the driveway and had the same symptoms except a puddle of gas formed and it was dripping from the joint between the manifold and the header pipe. The intake had puddles of gas in it as well.
I'm assuming something is completely shot in the carb...either the metering jets or the power valve but I'm not 100% sure it's a carb problem. Could this be a symptom of a plugged exhaust system?