So I chose the following route: I deleted the file in the Finder, emptied the trash the usual way, and then erased empty disk space with Disk Utility. This did the trick in half an hour.
I chose the fastest method in Disk Utility, i. e. overwriting only once. But frankly, except for the most paranoid this should be safe enough. (Wright, Kleiman and Sundhar have thoroughly debunked the myth about having to overwrite files several times).
It might not even be that the Finder is really inefficient in what it does, but that its default is possibly overwriting seven or 35 times. So changing that default (hidden prefs, anyone?) could then actually make the Finder faster for that purpose than Disk Utility.

