How to safely transport a heavy item downstairs

Measure from the top of the bottom sash to the top of the window casing. Get two pieces of wood about 2" by 2" and long enough to reach from the sash to the top of the casing. Cut them long enough to be a tight fit. With the wood wedged in the a/c unit should be secure. This also works on first floor units where added security is a factor as the window cannot be easily opened from the outside.

You didn't mention how you're using the ratchet straps, but from your concern about slipping, I think it's possible that you could be using them to better advantage. So I apologize if this is what you're already planning to do, but just on the off chance it isn't...

For the MDF, you want the straps going over the edge of the MDF and running straight down to the load boar, so the force is all pulling straight downward. The way to do that is one strap per load bar, in a loop, with the joined hooks and the ratchet mechanism on the same side of the loop. In the following sophisticated CAD rendering, the Sharpie represents one load bar, the Post-It Notes represents one end of the MDF, and the rubber band represents the looped ratchet strap:

This approach will clamp a low, flat load very securely in place. With the straps snug you shouldn't be able to budge it at all. Nevertheless, stop to inspect the load carefully after five minutes and regularly thereafter, and you're right to worry about the parachute effect.

If you're not comfortable with what the load is doing on the highway, hit the hazards and slow down. If people can't pass, pull over every few minutes.

To make the loop, you join the hooks by putting each hook through the eye part of the opposing hook; under tension, that'll be secure:

That ought to work for the door too, but a glass door be a lot heavier than the MDF, and assuming the edges are plastic or aluminum or finished wood, it'll likely be smoother (i.e. less friction against the straps). Finally, it's a much longer drive. So I'd want at least one strap securing the front of the door to something under your front bumper, for insurance against sliding back under acceleration. And then another to the rear, to guard against hard braking.

I can't say for sure how you would secure those end straps without seeing the door. If the door is mounted in a frame, you could loop them around the lintel and sill parts of the frame. To avoid contact between the hook and the frame, tie a figure-8 loop in the strap two feet from the hook, run the hook end through the door frame, and hook it onto the loop. You may need a pair of extra long straps for that part. You'll need to keep the strap under tension for this to be secure, and remember that the rear one may be out of view so you'll have to get out and inspect it regularly. Also if the rear end of the door overhangs the rear bumper, as it probably will, then the rear strap can't resist forward movement except in a disaster where the whole door comes completely free. Then you're just hoping to slow it down a bit. So if a forward movement will slacken both end straps, you must keep a close watch on the front strap for slackening.

And here's how I'd put a strap around a bundle of 2x4s on top of the MDF. The loop clamps them together and also grabs them to prevent sliding back. Note that the loop is arranged so the strap crosses at the top, not the bottom. That method would work with sheet goods as well.

I would also consider renting a U-Haul 5x8 utility trailer for the door.

Using a trailer for the lumber also would be safer, much easier, just as secure, not much more expensive, but infinitely less fun. I hear there are some weird people who don't think securing large things with ratchet straps is fun. But that's just weird.