Went thru this on a customers 62....started kind of out of the blue for him. Hard starts....just crank and crank and crank. Usually after he drove and parked. Cold starts seemed to be good. We had been progressively going thru the system on his truck since we don't know the history(185k miles) of it. Fuel pump and sock, regulator, pulsation dampener.....filter. It was kind of isolated but as it became frequent, we dove deeper. Each time we would see the truck and do something, it would change a little. I seem to remember fuel pressure loss at the rail being within spec when we tested(we would always find low or no pressure in the rail). We did find a lot of raw fuel on the number 5 cylinder's spark plug after we would crank and crank. Out came the injectors. We did those and the truck ran better than it had ever run.....MPGs and power were both way up. Really big change.
We install al lot of 3FEs in 40s....we go thru them from top to bottom so we never have issues like this but they alway have new injectors along with all the other usual suspects....pulsation dampener, regulator, filter, rubber fuel lines, fuel pump, sock, etc.
Also...have a look at that cold start injector.....they get horrible dirty. Important part of the system.
If you do injectors, make sure you get replacement connectors as they will be brittle and break. Easy to replace when you have the injectors out. We have a source for them. I seem to recall there are 2 different style plugs for the injectors.
The last thing we did to that truck after the starting was solved was replace the charcoal canister.....the truck would have a lot of pressure at the tank once everything was up to snuff. Replaced that with a generic Napa one and the truck has been spot on since.