I was troubleshooting a similar issue with 2BDE code before I totaled my car not so long ago.
Never had it shutdown on me or throw a limp because of that though. All it would do would have long cranks on startup but then rail pressure was super healthy so I was doubting that it would be HPFP. I read up a bit and decided to change the fuel pressure regulator but it didn't fix anything.
Was there any other codes when it limped? It's odd that it didn't start for a few min but when you let it rest (or cool?) it then worked. Potential cause as you pointed might be overheating electronics? Would the LPFP install request higher current loads making the EKPM3 heat up quickly?
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TOTALED | 2011 E90 335i xDrive - BMS Cold Air Intake - ETS Charge Pipe - ETS 7" FMIC - MHD Stage 2+ - GFB DV+ - PE Mod - VRSF Catless Downpipe - xDelete - xHP Stage 3
2015 E84 X1 35i M-Sport
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