I was working on a fork lift with similar problems it might be a long shot but the only way I could get it to start when warm was to pour cold water over the rotor head (the back of the pump where high pressure pipes come off) I think that is what it's called anyway.

I think the pump must not have been able to create enough pressure to open injectors after heat expansion.
The company didn't want to buy a new pump or have theirs repaired so they have strapped a watering can to fork lift

HTH

James