cherrybim: The Pri Chodosh, Beis Yosef, Rashba, and perhaps Ramban (on second read, I’m not sure what his bottom line is.) In fact, some (or all?) of them seem opposed to any custom, including doing it with money. But of course my point above was to defend the heilige minhug (not that it ultimately needs my defense), rather than to engage in a halachic discourse upon it.
The Arizal brings the Kabbalistic ideas of this minhug down.