Travis, I agree with Reggie - make sure the ignition system is working correctly BEFORE tearing into the fuel system (I can't tell you how many times I blamed fuel systems, for running problems only to find out it was the ignition!). To test for spark, unhook the high tension (spark plug) wire from the coil to the distributor. Place the distributor end of the wire near a ground (about 4 mm or 1/4 inch) — note that the rubber boot may prevent a spark, so use a screwdriver jammed into the connection if necessary and have the shaft of the screwdriver 4 mm from a ground. Have a friend crank the engine while you look for spark. Do this test both when it starts well/cold AND when it dies when hot — compare the differences.
Even if you do see a spark, replace both the points (gap them correctly, and be sure no oil or grease gets on your point contacts) and condenser anyway — very important — it's an inexpensive way of isolating the ignition system in your overall diagnosis (NOTE: To illustrate how, even when you have spark how sensitive ignition issues can be, I had an engine which would NOT idle smoothly (of course, I blamed the fuel system, vacuum leaks, you name it)!. I had spark at each plug (so assumed the ignition was in good shape), but in desperation (after almost replacing the carburettor) I finally replaced the spark plugs. It turned out that the shop who last tuned the engine (this was a Range Rover V8) had installed the wrong spark plugs. Installed the correct plugs, and voila - I had a beautiful, dead smooth idle. So, just having spark is not enough — you need the "right" spark! Recommend you isolate any chance of this being an ignition problem before you do anything further with the fuel system.