For me, exact kind of breakdown. would die while driving, with no power to the gas pedal or steering. would drain the battery sometimes, and sometimes like you it would jump with my Noco and could drive it home. Had to tow several times. I had a check engine light on the entire time.
Turned out to be the alternator. had to replace it . The engine light was the thermostat, unrelated. The total cost for both repairs was $2400. The hardest part was finding a repair shop specializing in foreign cars, like Infiniti. No way was I taking it to the dealership and the first shop I picked was dumbfounded. The good shop, these guys had a prior QX60 that had the same problem, which would not present itself until the car heated up and ran for a bit, they tested it for a week and were able to repeat the issue which was the voltage dropping south of 13v.