Ah yes, I seem to remember making a hash of a presentation of that argument a few years back and being brutalised (completely fairly) by none other than burrahobbit!
It still lies somewhere on the Downs...
'Tis a brilliant site
tgwbs.
But on topic: I had always thought that the House of Tom Bombadil was a dream. As we know the Hobbits were trapped by the Barrow-wight in the Downs. They were put to sleep; so it seems clear to me that the shenanigans did not actually happen in reality. I mean, Tom Bombadil and Goldberry
do not make sense! Wild nightmares are the obvious answer.
As for Fatty Lumpkin, I imagine the Hobbits just found him in a field somewhere.