Tow company damaged my transmission

There's something else wrong here. It's possible something got lost in translation, but the type of damage you described cannot be caused by towing. Everything having to do with reverse or forward gears requires one or more of the multiple clutch packs to be applied, and that requires fluid pressure to squeeze the clutch plates together. That requires the transmission's pump to be running, and that requires the engine to be running. They would have had to tow it with the front tires on the ground, the engine running, and the transmission in gear.

What could potentially be damaged, since it sounds like they had to tow it with the rear tires off the ground, is the park mechanism could have been broken. They needed to put the transmission in neutral to tow it that way, otherwise the front tires would have skidded all the way to where they towed it to. A lot of cars today need the key in the ignition with the engine running to allow the transmission to be shifted out of park, but if they couldn't do that, they sure wouldn't have towed it with skidding tires. They have "dollies", which are wheeled plates to place under any wheel that won't spin while they tow the car.

Most towing companies today use flat-bed trucks instead of the older-style tow trucks. Even with those, if any wheels are locked up, or the transmission is stuck in park, they can still pull the car onto the truck with a winch and cable. Transmissions are tough enough to withstand being dragged that way for such a short distance. The force on the parking mechanism isn't much more than when it has to hold the car when parked on a hill.

If they think they damaged something, it is much more likely to be related to something outside the transmission. That would include the cooler lines going to the radiator, and the shifter cable. At the age of your car, even the transmission pan is likely to be rusty, and bumping it or dragging it onto the truck could have caused it to leak. Some gears might work yet if all the fluid hasn't leaked out.

As for used parts, there's usually nothing wrong with them, except you're right about the repair quote being too low to involve work inside the transmission. If a rubber hose going to the transmission cooler is torn, you want a new one for that type of application. No conscientious mechanic would put a used hose on. The cost of labor is the biggest cost, and to save a couple of dollars on the cost of the hose is silly when there's a good chance he will have to do the job a second time. A used pan is okay as long as it looks reasonably rust-free. Internal transmission parts are hard to come by. That requires someone at the salvage yard to drag the car into the shop, remove the transmission, (a really big job), then they have to take it apart to get the part you need. That leaves them with a transmission they can no longer offer for sale. To cover part of their labor cost, you could pay a couple hundred dollars for a three-dollar part.

The better suggestion is for you to visit a local transmission specialty shop and get their opinion. Any problem you can think of, they've seen it before, often numerous times on the same models, so they will have a better idea of what was damaged. If they agree the transmission could not be damaged this way, we need to look for exactly what did happen, then figure out if it could have been caused by towing. If there is some common failure they run into often, they will know what parts are likely to be needed, and they often collect them from junk transmissions that are being sent out to the metal recyclers.

I have a suspicion the towing company only admitted fault to try to help you out by getting their insurance company involved. Please keep me updated on what you find out.

That was the second opinion I suggested. You got it already. You're listing a typical cost of a total rebuild, which shouldn't be necessary, that's why the cost they told you is lower. I agree they should have put the transmission in neutral to prevent the tires from skidding, but if they didn't do that, the tires would have flat spots worn into them.

The only other thing I can think of is if they did put it in neutral and towed it a long way, every manufacturer warns against that because the bearings the axle shafts run on won't be getting transmission fluid pumped to them to keep them cooled and lubricated. They typically say to limit towing to less than around 30 miles.

Regardless, if you feel the car is a pile, perhaps the better suggestion would be to take what you can get and think of this as an opportunity to find something you like better. I've had cars already where I kept throwing money at them, and it still turned out to be a waste. Try to not fall into that trap.