I personally wouldn't do it. Even if you could find a suitable hatch, you'd need a good way to clean it out regularly. When I lived in an apartment complex with a hatch, it was foul; it was bad enough that they'd spray for bugs every 3-4 months, and in the process, drive the bugs into other apartments (and mine was right next to the chute ... so make sure, when renting an apartment, take that into consideration).
I'd be afraid that if the chute went straight outside, that bugs would eventually use the route to come up into your home, particularly of any food trimmings were to smear themelves on the chute or hatch.
If you were to connect it to a garage, I'd be concerned with fumes coming into the house. At a bare minimum, I'd make sure to have a CO monitor inside the kitchen, but I'd think that car exhaust would get in, too, and might make for a less than pleasant effect on your food.
I'd also look to fire codes in your area -- you're not allowed to have open holes between floors in many areas, because it'll allow fire to spread more quickly. (never mind that you have to vent toilets ... but you then have to fill gaps on the holes those vents run through).
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For non-meat or dairy food scraps, you can also get kitchen compost bins which have a charcoal filter on top ... so you can stash your trimmings under the sink, and then empty it less frequently. The only real problem are meat scraps; yes, you can put them down a garbage disposal, but it's not ideal as it puts a greater load on the sewage treatement plant; also, it won't work if you have a septic system, and still won't provide a good solution for bones.
This might not be the answer you are looking for, but depending on the amount of moisture in the garage, why don't you just run a de-humidifier? I have one running in my basement, which gets very damp without it. I bought the one with the smallest container, since I'm bypassing the bucket with a garden hose straight to the floor drain. I have mine set a little high at 70% since that seems to be the threshold to the bad smell that comes from a musty basement.
If you get a newer, more energy efficient model, you will save money on your electric bill. Not to mention, it will probably be cheaper than your other alternatives.
Best Answer
Just build the platform as Chris Duffin did, make sure it is low enough so your auto's undercarriage will clear, and leave a couple channels/slots for your auto to pass through. You could make hinged lids that fold back down when the car is gone, giving you a continuous level platform surface. Keep it simple.