When I bought my rex, it didn't have a cat, and I was having the exact same problem. I would actually see soot spots on my garage floor from starting the car! I put a cat on there, and didn't see too much buildup anymore. Then I swapped the engine and haven't seen a bit o crap building up in there.
I'd check or replace the cat, and then check your timing. If your timing is okay, then u may need new spark plugs, wires, distributor rotor, cap, fuel filter, possibly a new evap canister, and for good measure, have your fuel injectors cleaned. That might sound expensive, but for all that stuff(except the cat and injector cleaning) your total will be around $70-100. Not too bad to bring up the fuel economy.