What part of speech do the quoted constructions belong to? [duplicate]

It's more than a hyphenated compound modifier (a to-do list). It's a stacked hyphenated compound modifier.

Bonnie Mills, at Grammar Girl has a relevant article, starting:

Today’s episode concerns a what-you-may-have-been-wondering-about topic. That sure was a mouthful, and it illustrates the problem of stacked modifiers, which occurs when you string together too many words to describe a noun at the end of the mouthful.

Though the examples given here are quirky, punchy and easy to understand, and fine in informal registers, caution has to be exercised to avoid confusion or silliness.

And I'd say that trying to analyse these nonce coinings as other than compound adjectives is a futile exercise (though their origins are transparent).

It is a hyphenated compound modifier!

How to stop worrying about compound modifiers Monday, 1 Feb 2010, by Linda Lowenthal -

http://www.copyediting.com/how-stop-worrying-about-compound-modifiers