Need advice on hot starting W460 280GE after shutting down for a few minutes.

My 1982 280GE starts fast when cold. But after driving for a while, if I shut down, it almost starts for a second, and then I have to crank for 20 seconds or so, sometimes pumping accelerator to get it to start. Thankfully it has a new battery, so eventually it starts.

For example, I will drive to the ferry... say 15 minutes. Then shut down for the 45 minute ferry ride. Then everyone on the boat - or at least those cars stuck behind me - hold their collective breath as it cranks and cranks until it fires up with a great noise. Alternatively I can spray some ether into the air intake, but this is a mission as well. One day, I fear it will not start, and I can't believe it is great on the starter to give it such exercise.

Clearly it is a fuel problem, but before I crack into it, I am hoping for someone to point me in the right direction. The petrol G has 400,000 miles on it, I've owned it 25 of its 40 years and the fuel pump buzzes when I turn the key, so I know it is pushing fuel in.

I don't know much about Bosch fuel injection, but am good with a wrench.

Ideas on what's wrong, and how to fix it, greatly appreciated.