If I were you I'd take the same approach as you.
A data backup and fresh install should be quick and free, it sounds like you have got nothing to lose (but your data) if your Prawn is practically unusable at the moment.
If this doesn't help I guess a new battery is the next step, either fitted yourself or return your Prawn to FxTec. I think FxTec still have some batteries for the Prawn, there has been some recent discussion between Prawnsters on the forum on this subject.
https://community.fxtec.com/topic/3326-pro¹-x-–-state-of-production-and-delivery/page/43/?tab=comments#