1. Get a Voltminder. Connect it directly to the battery and it will give you a accurate read of what your battery level is at. It has a low battery alarm that you can set.
https://www.amazon.com/VoltMinder-Digital-Volt-Meter-Batteries/dp/B001IQ1XW42. If your draining two batteries in two days you have a significant drain. If you use your furnace batteries won't last long.
You will need to run your generator longer. Watch your Voltminder and try and keep it between 12.4 and 12.7 when not charging and batteries rested.
3. Add more batteries. Two group 24 12 volts will have about 170 amp hours, two 6 volts will have about 220 amp hours. If you add two extra batteries to the two you already have you will double the amp hours. You can see you will end up with more amp hours with 6 volts.
4. Solar would be nice but you will need at least 300 watts to do any good. That will cost you around $1000+