Product review (5 stars): Throw it in the washing machine
On a whim, I threw this in our front-load washing machine on the 'gentle' cycle.  The glue that holds it in a circular shape did let go, but other than that it came out in decent shape.  I was able to put it back in my humidifier (I have the style where the filter is surrounded by a plastic ring that helps it hold its shape, so I didn't have to worry about the glue letting go) and get another week of use out of it.

To get the most life out of the filter, I also recommend that you don't run the humidifier full-blast all the time.  Set the humidity level such that there are gaps in the fan's operation.  This allows the filter to continue to wick water all the way to the top, and prevents a ring of minerals from forming half-way down as can happen when the top half of the filter never gets a chance to suck up any water.