Like jbizzle said, there's just no way around it. Clogging is good! It means the stuff that used to be in the pool is now trapped in the filter and can be rinsed out. Either patiently filter it out or drain and start over. Draining costs $$$ for new water and chemicals though.
You'll just have to put up with cleaning the filter daily, twice daily, whatever it takes. Either that or spend more money on a larger cartridge filter or sand filter - but that's just a waste of money.