[Daox]

I would keep it simple (and cheaper) and go with lead batteries. I would not go fancy with AGM or gel, just a regular flooded lead acid deep cycle from the local store. No BMS required, the charge controllers are cheap. Everything is readily available should you need to replace things. I'd oversize it generously for the cold.

Also, I think your calculation of the amps is incorrect. Allow me to try to clarify. A 7Ah battery should be able to supply 7 amps for one hour. That means that it should theoretically supply 9 amps for (9/7 = .78) .78 hours. Or, if you pull 5 amps it should last (5/7 = 1.4) 1.4 hours. In reality its less than that, but that is the extremely basic calculation.

If they have two 7Ah batteries in parallel then you have 14Ah of capacity. They even claim this isn't enough. I'd get a recommendation from them on how many Ah you need. Conversely, you can just figure out what you can get cheaply locally. Something that does 30+Ah sounds good to me though.