Hi Christoph,
did you see http://service.sap.com/sap/support/notes/1935085?
You talking about starting PI when backend system is not running got me curious. Maybe this is the same problem that we are facing, too.
Could you please check if your XI ADAPTER FRAMEWORK 7.31 is below the mentioned patch level of the note? If so, the note may well solve your problems. At least I would provide SAP with this information in your ongoing support ticket.
I could say for our system, that for XI ADAPTER FRAMEWORK 7.40 we are currently on SP 5 Patchlevel 0 so the note would apply for us. Currently checking if update is feasible.
Thanks and kind regards
Jens