I’m not sure what you mean by “regulated”. Regulated in what way? 12v doesn’t need to be regulated. You mean like pure sine wave?
There’s a couple things that could be happening. First, 10v is NOT 60%. That’s straight up dead. It could be that it’s sampling voltage not on a shunt. That would cause the voltage to drop while it’s under load. It’s also possible you’re just not charging it enough. But most likely your battery is just toast.
DO NOT buy a boost converter, that’s not your issue. 12v batteries don’t go to 0 volts! Anything in the 10s may not even be recoverable and you’re probably irreparably damaging it every time you take it that low. Also keep in mind, you got like 30ah with that thing. That’s just not very much. Your fridge consumes 50 watts by itself.