150-160rpm sound too low for hot start. On 1.9TDI which experience similar problems it needs to be 250-280rpm when engine is hot. Have you had your battery tested or replaced? Considering that it turns faster and starts when jumping it tells me that battery is too weak as that's the only thing that changes.
Another thing you could try is to unplug coolant temperature sensor when it's hot and refusing to start that way ECU will not know temperature and may allow to start injection at lower rpm.
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Currently 8less
2011 Q7 S Line 3.0TDI, 2016 Tesla Model S 90D
8 history:
2006 A8 Sport 4.2TDI quattro SOLD,
1997 S8, reached end of life with gearbox failure
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