Couldn't be published these days? I think Light would take it in a heartbeat.
For that matter, if Odgen were still alive, he'd be selling on his name alone and would have it in the New Yorker.
Anyway, I'm not certain what you mean about the long line or even stylistically. This is anapestic tetrameter with some iambic substitutions, or you could just count it as accentual syllabic as tet as well.
In fact, I'm kind of amazed at this being thought so unusual, since I had a poem a few years ago published with almost exactly the same meter,
"Ferdinand Feghoot and the Zero-G Nunnery" , the only difference being that I used some feminine line ends, going dactyllic instead of anapestic, and had five stanzas of ten lines each instead of seven of eight as Nash has here, but fifty lines of dactyllic tet versus fifty-six lines of anapestic tet, all done in couplets?
But anyway, thanks for showing the Nash poem. I hadn't read it before and it is great fun.