I did something similar but my all in one unit (smart charger, auto transfer switch & inverter) had one component fail so it was either replace all with another all in one compact unit or use individual components. I decided to use separate components. After several years of use, I decided to remove the Auto Transfer Switch aspect altogether. Just slow charge batteries continuously with a smart charger (to prevent overcharging) and inverter. When the power fails, the batteries are already full. I also switched to lithium batteries which can be depleted much lower than 50% discharge, much lighter and more reliable but quite a bit more price wise. I suspect that's why your used deep cycle batteries were available.

The other thing I do is only back up my airpumps. Everything else can wait until mains power returns or I manually connect up a generator. I can go several weeks safety this way.