Many thanks, Tony.

Here is a blue clicky for the ebay record: Ebay item

This site gives a date of 15 January 1919 for the Norworth recording. [You need to scroll down or do a search].
Norworth record.

On this evidence, it appears that the poms composed the original and the yank did the nicking and added verses.

We would still love to see the complete lyrics for the Norworth record.

--Stewie.