izeman said:These little boards claims 4A output. Sure this is chinese amps, and it will not work converting 5V to 30V@4A, as it's the input current AND the output current that count. But if you say your working battery range is from 9V to 12V and your output is 2A@12V you should be fine.
You can then decide if it's better to down convert 4S to 12V or boost (non fully charged) 3S to 12V.
https://www.aliexpress.com/item/DC-DC-Non-Isolated-Step-Up-Module-4-5V-32V-To-5V-42V-Adjustable-4A-Boost/32832844122.html?spm=a2g0s.9042311.0.0.140b4c4dTy5a0W
I have some like that and I think they would be good for this application. Only thing is it will either need to be always on or get switched on when the power fails. I guess it would work to be always on and keep a 4s pack at 4.1v/cell with a power supply that is current limited to a safe charging current.