Hello Michael,
I too would be tending to discount the battery and indeed the starter motor since you say it appears to start OK from cold when there would be a far greater load on these components.
Of course, it's always difficult to diagnose these problems, but it could (just could) be an injector/s at fault and perhaps giving you symptoms of "misfire". As I understand it, even one faulty injector can have a significant influence on how it starts and runs. Not sure if this would show up on the diagnostics, but failing that it would be a question of having a leak- back test on them, and if any issues, taking them out and having them checked - not too expensive to have them checked.
Good luck with sorting it.
Kind regards,
Gareth.