Route out the back leaving a little less than what the clips can handle.
If you don't have a router, you could use a face-mounted bezel to hold the controller. You'd just need a slightly bigger hole through the collar...
Have you cut the hole already? If not I would just put it in a project box. Cutting extra holes in the collar is just more lost insulation. While many people do it successfully STCs arent water tight or designed to be in an area where condensation is more than likely.
If you have cut the hole you could prolly find a small C clamp at a big box store to clamp both sides of the stc inside the collar so it doesn't slip out.