I really don't think there is the slightest doubt that Henry Clay Work wrote both text and tune of "Grandfather's Clock." Work was a brilliant composer of tunes:
Kingdom Coming/Year of Jubilo
Marching Through Georgia
Ring the Bell, Watchman (=Click go the Shears)
The Ship That Never Returned (THe Wreck of Old 97/M.T.A/The Flying Colonel)
What's more, every description of Work was of a very quiet, moral, honest man (an abolitionist, e.g.). There are no other reports of him borrowing a tune.

There wasn't any reason to, either, since "Grandfather's Clock" was something that he didn't try to sell at the time he wrote it -- songwriting wasn't paying well enough to bother with it; he only published it because Chauncy M. Cady asked Work to write some songs to help Cady re-establish his business which had burned down. (That is verified not only by Cady but by George F. Root.)