Hybrid Battery Charger Question/Idea
You would have to see the circuit diagram, but, normally, I would expect that this 12 volt output was a one-way arrangement where you couldn't feed power back the other way towards the big battery.
It is not all that difficult to produce 350 volts from a mains supply for charging purposes and it is surprising that nobody does it at a reasonable price.
There are issues of safety, of course, but these could be overcome fairly easily.
Maybe the prices get inflated to match what owners are prepared to pay.