Long crank is usually indicative of HPFP... I have had the same issue intermittently. The annoying thing is that the stealership won't replace it under warranty unless one of a few specific codes are thrown (sorry, don't have them on hand).
The code you got could be indicative of a leaky injector. On my car this expressed itself as a rough cold idle after the car had been sitting overnight... but not necessarily a P0175 code. Replacing injector(s) is a pretty easily job, but requires a special tool to mount and compress the new gasket (which MUST be new). I replaced all six with "rebuilt" (probably just lightly cleaned) injectors from eBay. These injectors have gone through a number of design tweaks over time, so if you want to install a factory-new injector you may actually need to do all six if the index differs by more than a few numbers. There are plenty of posts on N54Tech about this.
Lastly, I found that after replacing the injectors, resetting adaptations in ISTA/D helped avoid some of the codes I got (e.g. low-P fuel pump implausibility). If you have access to ISTA, give that a try before even installing injectors.
"Sabine": '88 M6 Royalblau/Silber
SLS delete, Wizard Cooling radiator, BavAuto Strut bar, M-Technik steering wheel, Conforti chip, Bilstein B8s / H&R lowering springs
"Greta": '00 M5 Titansilber / Grau-Schwartz
Euro Hellas, e-Light control module, muffler delete
"Cosette": '09 335i Titansilber / Schwartz
Just trying to keep the stock N54 running without throwing codes.
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