How nice to come to the end of some comments and see a series of replies that sums up the discussion and even provides some closure:
Owen: "Some things seem like they would be hard to do with using a verb."
lornajane: "To do it RESTfully, you just need to rethink your url and put it into a form that is supported by PUTs and POSTs, etc..."
Chris: "Then I probably shouldn't use REST in this case, since doing so would sacrifice clarity for correctness."
I think all of this is correct, and I come to the same conclusion that Chris does. To completely misquote Isaac Asimov: Never let your sense of what's correct get in the way of doing what makes sense.