Roy Palmer gives a transcription of Arthur's singing on the recording, the tune and a facsimile of one of the other sets of words.

Palmer, Roy (2004) The Folklore of Shropshire, Logaston Press, ISBN 1 904396 16 X.

The main differences from the words given in the first post are:

V3, L3 "Condemn", not "commend"
V3, L2 "else we should starve"
V4, L2 "God's civil mirth" not "good civil mirth"
V4, L3 "hymning and singing" not "ringing and singing"
Last line "and now if you please, ma'am, we'll taste..."
Spoken "Happy New Year! Happy New Year!" at end.

Palmer writes verses 3 and 4 as a block of 8 lines so maybe something in Arthur's delivery supports Steve Gardham's suggestion above.

To me V3, L3 was the puzzling one in the written words, they all have "commend"

The written words all clearly have "good civil mirth" and "ringing and singing" which is an interesting change given that ringing features prominently in both what Arthur said and in other local accounts from the 1800s to the 1950's. Arthur had sung in church choirs since he was old enough to sing.

I'll be back with the tune.