Here's a new one, not found in any dictionary. It is in today's paper; is there any prior print usage?

... reformers ought to throw their energy into that idea, rather than to the windmill-tilt of trying to purge money from politics.
Wall Street Journal, June 29, 2006

Don Quixote tilted at windmills

tilt at windmills@Everything2.com To tilt at windmills is to confront and engage in conflict with an ... The title character, Don Quixote, attacks a group of windmills with his lance at full ...
everything2.com/index.pl?node_id=424145

The abbreviation of tilt at windmills to "windmill-tilt" seems a bit strange, however there seem to be few options in this sentence. There is really no good good way to say tilting at windmills. Furthermore, the process of changing tilting at windmills to windmilt-tilt seems a fairly productive English process.

Of course, you could say "rather than quixotically trying to purge money from politics", but that would be too easy.

An easily understandable (by its target audience, anyway) metaphor, although unremarkable. As Seanahan says, you could use "quixotically".