Ben,
You have received very good advice so far. One question, is the rubber pump cup on your accelerator pump black? If it is, these cups usually have a short life when exposed to racing fuels. Like Mike mentioned, C-11 is the toughest to deal with because it even seems to leave a residual film inside the carb when it dries. If you have the black cup, I'd be happy to send you one of mine to see if it helps.
I would also recommend that you take a look at the check ball and the seat that it sits in to make sure they are clean. If the check ball is not sealing properly, the upstroke of the accelerator pump could be sucking this circuit dry. I can give you some pointers on how to check this if you want me to.
Keep in mind also, the bowl area of a Q-jet is very small, so if the car sits for a couple of weeks most/all of the fuel inside the carb can be lost to evaporation. If this is the case, then the carb is simply "empty". However, this leads to the situation described earlier where the pump cup will now start to dry out.
Dean Oliver
www.deanoscarbs.com