The reality is even with a poor converter, two batteries should have taken you through the night after a 6 hour run of the generator. We did season on the generator a few hours a day with a even worse converter and never saw the single battery get below 70%. We saw freezing temps nightly all but one trip mid summer.
You will get great advice here if not a bit gruff at times. With enough cash the guys here can help you set up the boondocking rig from he:: but I suspect the first thing that needs to be changed is your charging regiment.
What I have seen in the thread is that your batteries have likely never been fully charged if you have only used shore power or the generator to power the converter. So even after a trip with shore power you park the rig and disconnect the under charged battery and let it stay like that until the next trip. Come the next trip you plug in the 7 pin and take off and honestly the 7 pin does very little charging. The batteries have also been allowed to become severely discharged which is along with the under charging a detrimental to the life of the battery. They may not be toast yet but they are damaged. Also while the converter will undercharge when cold, it will cook your batteries dry in the heat. You have to make sure the water level in the batteries are up.
One thing I haven't seen asked is how big are your fans that run constantly and how many amps do they pull?
Now I don't have many of the fancy toys suggested here so my charging regiment is different. My batteries come home with me to be maintained. Once the water is checked, they are put on auto chargers for 3 days after a trip. If a month goes by without us camping I put the chargers on them for a day, I put the chargers on 3 days before we go out again. Since we have solar we haven't used the generator while on a trip for a few seasons.
So get the batteries off the rig, get a jug of distilled water and make sure they are at the right levels. (if the water is below the plates it is not good ever) Make sure your cables and post are clean of corrosion, Put each on a stand alone auto charger for 3 days, let rest a day and with a digital volt meter see what they read. A fully charged battery should read 12.7v. Should one or both batteries read below that, they have lost capacity. It may be regained but with what you have described a better bet would be a new set. Even if they read good I would have them load tested or check each cell with a hydrometer.
All just suggestions, I wont horse whip you if you don't do it. ;)