Is this a thin window air conditioning unit

You could build a wood frame that fits in the window with an interior hole large enough to accommodate the AC unit. This also has the advantage that you won't have to hold the window open, while juggling the unit into place. You can install the light weight frame, then slide the unit into place.

I built one when I lived on the second floor of an apartment building, because I was always afraid I would drop the unit out the window while installing it. I used foam tape around the exterior and interior of the frame, to make sure I got a good seal around the window and AC unit.

For a unit that only vents through the window (not sits in it), you could build a smaller frame with a port to allow the vent to pass through. Filling the interior of the frame with Lexan will reduce the amount of wasted window space.

(You could always use smaller lumber for your frame, if you want it to have a lower profile. The frame size in the image is just an example, to illustrate the idea).

Divert some of the A/C output air toward the thermostat sensor. This should cause it to shut off sooner and raise the low end o9f the hysteresis. It works like an anticipator.