So I picked up some fuel hose to replace the pieces before and after the filter in case that was the source of my chunk of gunk. I installed the hose pieces this evening, started the car up, and had the same symptoms. Pulled the fuel line off the carb, took out the needle, and found another piece of gunk. I removed it, put everything back together, started up the car, and it ran fine. Here are some possible sources of the gunk, which again seemed to be a piece of rubber:
1. This last piece was one last piece from the old hose, and now my problems should be over.
2. Its originating farther upstream and somehow getting through the filter, which would make it the crappiest filter ever.
3. Its some rubber piece from within the filter, which would again make it the crappiest filter ever.
4. Could it be coming back up through the return line??? I know some Eagles came with a check valve in the return line (there was not one present in this car when I changed the line), so could gas and gunk be coming back into the filter and then into the carb??
My plan is to pick up a new filter tomorrow, put that in, and hope my problems are over.