If the tree is not in danger of coming down on a building, just let it be and tap it until nature takes it course. I do not make a habit of cutting down a tree until I can not get any more sap out of it. Just because they are old and not so nice looking doesn't mean you can't tap them.
30x8 Leader revolution, wood fired blower, steamaway/hood. 903 taps all but 54 on pipeline and 3 vacuum systems. Hauling sap this year with a 99 F350 7.3 diesel dump and of course back up is the Honda 450 and trailer.