Nice story, I think it is not so bad it would stop on idle during flare, because it is running bit rough on very idle, but still not SO bad, it is way better when leaned, but still not so big deal.
I never use aux fuel pump, only for priming engine before start (Reims Rocket). Maybe there is aux fuel pump only for situations, when main fuel pump fails, injection needs pressurized fuel and only gravity feed is not sufficient for engine run. So the aux fuel pump is backup for main pump. Even in POH is mentioned only for starting engine.
This is from POH
The aux fuel pump on injected high wing engines is used for starting the engine and potentially in case of ‘emergency’ (ie engine not working properly, you can try to use it, see if it improves anything)
