Can't really answer your question without knowing more about the Truma system. Can't find any power consumption specs nor BTU output. Only info I could find is that it runs about $1500.
Other thing I would need to know is how much aux power you need for computers, tv, etc. If you are light on those (say 1hr/day) and assuming the Truma consumes the same power as a regular furnace, you should be able to get two possibly three days of boondocking in clear weather with that system before you need alt source.
Usual rule of thumb is 100 watts solar per 100 amps of storage for short term. Idea is that 100 watts will average about 60A/hrs per day while a battery drained to 50% will require 50A/hr. However, those numbers assume you don't have a large requirement during the day. With the compressor fridge, you should consider a 3rd solar panel so it will provide the necessary power for the fridge during the day which is usually it's highesst demand period since that is when it's the warmest. With the lithium batteries which you may drain deeper than a standard battery, it will also help recovery. Of course, this assume you are in a sunny environment.
In regards to the batteries, since you are going lithium, make sure you put them inside where they are in the climate controlled space for better performance along with one less leak and insulation hole in the outside wall.
Edit: Finally found a few specs for the Truma 4E version but they should all be about the same. While the power consumption is less, the heat output is less so it's going to run longer than a standard furnace. The assumption to use the same power consumption above as a standard furnace is valid and on the safe side.
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