Not only does the stanza fit the tune of "Strike the Bell," the words themselves suggest it.

I agree with Gibb: "playing" shanties must mean a musical accompaniment and, unless used for heaving, "Strike the Bell" isn't a shanty.

I also agree with Charley. If you want to turn a shanty fragment into a new song, go ahead. That's what happened to "Hullabaloo Belay," whose rousing tune would have been completely forgotten otherwise.
The newly refurbished song will inevitably be accepted and represented by others as the real thing straight from the fo'c's'le. Like "Hullabaloo Belay" and some others.

But maybe keeping the facts straight will provide 22nd-century scholars with something to do.