Good show, Alec! Abby is absolutely right that Henderson's involvement has nothing to do with the significance of an unpublished text contemporaneous with the times. If changes were made to Henderson's song so soon after its composition, then the version you found is even more of a folk song. If Henderson polished up an original such as yours, that woul be even even more interesting.

Here is a stanza I haven't seen elsewhere. It appeared in one of Eric Partridge's books maybe 45 years ago:

We fought 'em on the mountains, we fought 'em on the plain,
We fought 'em in the sunshine, we fought 'em in the rain.
We didn't want to go and fight
In all the mud and all the shite,
We are the D-Day Dodgers, out here in Italy.

Pre-Henderson or inspired by him ? It doesn't matter very much.