Your proposal, Morbius, was that
tangoed and
tangoes should have the same classification, but I don't think anyone would suggest that
tangoed is not common, so the issue really is whether
tangoes should remain rare or be treated as common.
It seems that people mostly write the inflected verb as
tangos, like the plural noun. Dictionaries give different advice on this.
I googled the quoted phrase "tangoes the night away" and got 5 results. Doing the same for "tangos the night away" got 38 results. For example, "Katy Perry Tangos the Night Away in Argentina" in the
Hollywood Pipeline in 2018.
We came up against similar issues with
radioes,
taxies and
soloes. In each case it was suggested that the verb was inflected by adding
es while the plural of the noun was formed by adding just
s. But it appeared that not every dictionary saw things that way, and in practice most writers leave out the
e, whether using the word as a noun or a verb.
Thus
I added radioes as a rare word. On similar grounds I think
tangoes can be left as a rare word.