I would probably keep working it down and see what happens, it looks like there is plenty of horn to work with, taper it more from the base up, thin is not necessarily bad. Not sure what you mean by checks but you could always shorten the base if need be to get rid of them. Or you could put a rawhide patch on the whole thing or just on the parts that need it. Copper, brass, pewter, staples,etc...could be used as needed.
Since it was free you haven’t lost anything, experiment with it, save the base for another.
Tim C.