The OED gives no explanation of the American usage of stave, as in the verse from Ground-hog, but gives several quotations beginning with the one from 1819. None has a plural usage.


(The Merriam Webster Dictionary gives the preferred plural of staff as staffs, with alternate staves.
Ground-hog does not seem to be an old song; not known from the 19th C., when 'staves' probably was preferred.)