Too much fuel to engine

Ignition module maybe ,watch this video ! ScannerDanner gets his but kicked by an 88 150 EEC IV Ignition

To clarify, you said it runs for 20 min then quits, and it won't start again until it cools off. Have you checked for spark at the plugs and fuel pressure right after it quits running ?
These models have an ignition module attached to the side of the distributor that has a history of failing when hot. The coil and the pickup inside the distributor can fail too. Could also be a relay.

If this doesn't do it, see my tip at http://www.fixya.com/cars/r5821173-doesnt_car_start_gasoline_engines . These are generic instructions. If you get stuck or need specific instructions for your car, please get back to me

It sounds like it might be runnig lean on fuel. How old is the fuel filter. Lack of fuel will cause this. Ford needs about 40 psi of pressure to run well. So it runs a lot of fuel thru the filter. It should be changed at least every 30,000 ?

make sure the air filter is intact and clean, the engine needs to breathe
do you have fuel pressure?
how about spark, do you have a good spark ?
change plugs and wires

Here's a trouble shooting check list. http://www.stangnet.com/mustang-forums/6161267-post.html

fuel pump

The jets in the carb are too big for a 302 with a stock cam. Take it to a carb shop and have them replace the jets with stock jets. (Or DIY and hope). Whne you converted from FI to carb did you replace fuel pump to get correct 7 1/2 psi pressure at carb inlet? FI pumps put out 50+ psi and a regulator maintians pressure at the injectors on the order of 35 psi.. Of course, that much pressure would force inlet needle valve out of it's seat and would probably flood carb totally, but, check the fuel pressure at the carb just to be sure. Good luck. 302's rule!!!!
PS - Check cam specs - FI engine has different cam - intake duration is longer if I remember correctly. Been a while since I got inside an engine...

replaced fuel filter yet ? have you checked fuel pressure and the fuel regulator

Check the basics, fuel pressure, fuel filter plugged, spark plugs, dirty air filter, coil output-use an old spark plug and watch spark intensity. Could be a plugged cat. Good luck!!