"Second possibility -the ecentric on the cam isn't functioning properly. (ok, how would you fix this?)"

To replace the fuel pump ecentric, you take the timing cover off. That is what Amervo is saying. Once you're that far into the labor, it is irrisistable to replace the timing set if it is worn. A new timing set would add ten minutes and $41.00 to the fuel pump eccentric repair job. While you're at it, you would also freshen up the antifreeze (which you have to drain to do this work) unless it is pretty new.

The original 350's had a nylon covering over the gear to make it run more quietly. This gear would strip and slip time, usually when you try to start the car while you are a long way from home. If by long shot your engine still has a nylon gear in it, absolutely ditch it if the timing cover is off.

I wouldn't be so quick to install an electric fuel pump. If something happens to the fuel delivery system in an accident or fuel line rupture, it will continue delivering fuel to any fire. This is why new cars have an impact sensor and interlocks that shuts off the fuel pump during a fuel delivery rupture or accident.

There is one more possibility you didn't list. It's possible that the new Autozone fuel pump is bad out of the box. It's a long shot, maybe wishful thinking, but new doesn't always mean good.

Your close to having it fixed, so don't get discouraged. Cruising weather is supposed to be nice later this week.