That will happen , dont forget that the 12.5 you see is voltage with the draw of the heater running which is probably about right , I would not buy a battery yet as you might be ok , what you need is a pal with a battery you know to be tip top good and try that
Did you say it runs no different if the van is started ?
You can just use plain old water to clean the plate exchanger from your garden hose sprayer but it is a bit of a faff , but if you take it off and try it will become aparent you got poop in it right away .
It could just be a single gasket that has gone in the exchanger , thats all it takes to knacker one as they are factory sealed , you could have up to 16 plates on yours I think