I've never looked at this but sounds to me like everything is about how it should be. If it was fuel pressure related it should have fired and cut out when pressure was up. I believe the ecu doesn't monitor fuel pressure so it wouldn't stop it starting and the engine would sputter rather that not start at all.
Any fault codes? Oil level OK?
An e39 is like a beautiful wife, needs constant attention, lots of money, lets you down at the worse times but you’d never be without it.