Yes I see the same problem, there is no problem changing the winding to 36v to charge a 36v battery but there is no common inverter available. In the old days there were a load of 32v appliances which would most likely have coped with 36v but those days are long gone.
I also agree with testing the battery on site with a hydrometer and voltmeter. If the sg readings are all low or very variable then it will be at the end of its life. If the cells have been below 1.8v for many weeks it will have sulphated and may never recover. If Sg is over 1.200 and each cell is over 2v then you are probably on a winner.
Another thing to look for is the signs of lifting the tops on the positive side of the covers. This happens when the positive plates start to expand and things are near the end of life. Badly bulging cases also indicate problems from plate growth.
Most are replaced when they no longer handle a days work. If all cells are equal it may still be useful to you for a few years. if there are a few cells bad you may get enough for 24v. If there already many bad cells the end may not be far away. still worth a try if cheap enough but it may be more trouble than its worth.
Flux