I had the same problem with my 2006 WK recirculation control.
You do need to pull the glove box, but thats not hard to do and there is no cutting required. I found the gear was broken in two pieces and since the dealer wasnt open on Sunday, I just JB welded the old gear back together with additional material to make it more like the upgraded gear shown in the attached DIY link. That was about 6 months ago and its still holding. The gear is just a push on/off fit on the actuator motor.
As stated in the link, the trickiest part is getting the gears meshed properly.