There has been far less research into the G1W series cap-powered firmware versus the battery-powered models. The G1W-S firmware with it's unique-for-this-series-of-cams Sony sensor will probably not be usable in any other cam and vice-versa. I could be wrong as this is not something I know a lot about.
The G1W series of cams are long in the tooth and as far as I know no new developments are happening with any of them. Unless you're willing to brick yours, the best bet is to use the firmware it has now. Of course if you try anyway, please share your results as there are still a lot of G1W series cams in use, and whatever you find will be helpful to others.
A year or so ago, I jokingly made the claim of being the last living G1W series dashcam fanboy in the world. Even I have given up on these now as for whatever price is being asked for them, there is a better cam selling for the same price. My advice is to use yours till it dies or gift it to someone when you upgrade to a better cam. No matter what you do with them they are not worth fooling with anymore.