If going to another battery, try to match as closely as possible.
My biggest battery saver when I started boondocking....LED bulbs AND energy management. It's cheaper to conserve than to buy more.
My experience with marine/deep vs true deep cycle is that they will sometimes get pretty lazy. It all gets into charging, equalizing etc. Bottom line is check your specific gravity. There are tons of posts by sketter, bfl, mex, niner, roy, landy, etc sorry to not remember more at the moment.
Point is you need to know what is happening with your battery vs converter output and length of charges. It's deep but it's also not deep. It just all matters though. More battery could result in more dead battery.
Instead of another battery you may even go to a small gen. Manage your times such as microwave use, hair dryer etc and run those things while also charging.
Get yer wallet out, ya just got started. :)