I have been following the threads on hot starts with some interest. In general, I think it is difficult to sensibly do anything other than what the "good book" says i.e. the flight manual. Allison and Bell probably know more about their engine in their helicopter than most other people.
My experience of the Allison 250 (mainly JetRanger) is that if you do not get in excess of 12% out of the battery, you will almost certainly get an aborted or hot start, and you almost certainly will not get an engine that you can go flying with. There is a bit more scope for modulation with a Ceco system.