Of course the SOLAR PANELs only work during the high sun period which is typically around 5-6 hours a day.
You will have to increase your battery banks to be able to use them for running heater fans at night. The Solar would be used to keep the batteries re-charged during the day time hours.
Based on my experience the furnace fan will drain one battery per night using the furnace fan all night. If you have two batteries you can hold out for maybe two nights.
We have 255AHs battery bank capacity on our OFF-ROAD setup and both an Inverter and direct battery connections can run most of all we want to have running in a one/day night run off our batteries. Then the game plane is to re-charge the battery bank back up to their 90% charge state the next morning using my 2KW Honda generator. With the generator running the trailer shore power cable using a RV30A-15A adapter the on-board smart mode converter/charger unit can be recharge my battery bank back up to their 90% charge state in as little as three hours starting at 8Am in the morning during breakfast.
This usually fits with the campgrounds that have generator run time restrictions in place.
Having solar panels installed will help in this situation by not having to use the generator as much to re-charge the batteries during the high sun day.
Using small solar panels for power to run heaters is not going to work well for you... You can only get around 5-6AMPS of DC current from a typical 120WATT Solar Panel when sitting in the high sun. When the sun goes down you will not have any SOLAR OUTPUT. You have to store what sun power you get into batteries to use later.
I would think Propane would be the best solution.. Consider this google search CAT 5 type propane heater install - Pretty neat... All you need is a cabinet door close to outside location for venting.

Just some of my thoughts here...
Roy Ken