First thing I noticed is you told nothing about your batteries.
Are they GC-2 pairs (Two six volt golf car batteries in series to make 12 volts)
or 12 volt MARINE/deep cycle, and if the latter Group 24, 27,29 31 or something else? It matters.. Just like flashlight batteries, You would not expect an AAAA (Yes that's 4 A's) to last as long as say a "D" cell..
So we do need to know.. Also have you checked, if they are Flooded wet cells are the plates covered with fluid (Acid/water mix) or are the tops of the plates exposed (Not good) if flooded fill with DISTILLED water to about 1/4" BELOW the bottom of the filler tube more or less is ok but below the bottom, not to the bottom..
And tell us more about your batteries.
OH, Very good choice on converter.