Advice for Appeal Process with AAA

I'm looking for some insight on a situation I have regarding the mishandling of my car on behalf of a tow truck driver sent by AAA. Let me explain the story to the best of my ability.

I live in Western NY and hit a pothole (no surprise there) on Feb 19th and the axle snapped on my driver side front wheel, which caused my steering to give out completely. Thankfully, I was close enough to my house to bring my car there without any issue. I had my mechanic come by to look at the car on Feb 20th to give me an estimate on repairs. He took photos of the damaged axle and determined I'd need to buy a couple parts. Seems reasonable and easy enough without needing to bug my car insurance provider, plus I was able to barter with my mechanic to essentially waive the repair cost. I needed to send my car from my house to my mechanic's shop, so I called AAA. From there I'd order the parts, ship them directly to his shop, and I'd be back on the road in no time, or so I thought.

So, my car gets transported to my mechanic on Feb 21st, and the tow truck driver had to remove the left front wheel to hook it up to the truck. When he dropped it off, he rested the car on a ball joint skate. The following day on Feb 22nd, my mechanic took a look at my car again to prep my car for repairs, so he jacked it up and noticed that my transmission was cracked open and leaking fluid. My mechanic took photos of the leaking transmission, it was not cracked in the photos of the original damage to the axle on Feb 20th. While we don't have clear video or photo proof of the way they unloaded my car (The tow drunk driver does though), it seems that the tow truck driver improperly unloaded my car onto the skate and the lopsided weight of my car on its left side pressed into the aluminum case of the transmission, causing it to crack. That's my mechanic's diagnosis as he doubts it was wrecked during transportation. I'm not an expert on cars, but that seems plausible to me. This is awful because transmission repairs are incredibly expensive and those kinds of repairs aren't covered my by car insurance. I called the tow truck company and my auto insurance and explained to them my situation, and they both told me to go through AAA claims.

AAA sends out a guy weeks later on March 18th to inspect my car for the damages. At this point, my axle has already been fixed and the wheel is back on. I was there with my mechanic when the claims guy showed up and this dude half-assed his inspection. He walked around my car for 2 minutes from a distance, did not look underneath car at all, and denied my mechanic's offer to jack up the car and take the wheel off so he can take a closer look. The claims guy said "he saw the pictures already" but didn't attempt to verify them. It felt like a slap in the face. A couple weeks after his inspection he writes this email:

"Dear (me),

Thank you for submitting your damage claim to AAA Western and Central New York. We take matters like this very seriously and appreciate the opportunity to review your situation thoroughly.

After a detailed investigation, we found that the damage reported is not consistent with the service performed during your Roadside Assistance request on Feb 21st. Specifically, this appears to be the result of an impact or an attempt to pry the remaining piece of the axle shaft out of the transmission. The way in which the driver both loaded and unloaded the vehicle, using a ball joint skate as the tire had already been removed, would not have caused this type of damage.

Based on these findings, we are unable to arrange reimbursement or repair in this instance. Please know this conclusion was reached only after careful consideration and review of all available information."

This is obviously BS. Not only was the investigation poorly conducted, the wording of their conclusion makes it seem like it was my mechanic's fault, even though he didn't touch the car until after the damage to the transmission had already been done. I'm filing an appeal with AAA now and these are the 2 prompts they need:

Please describe why you're appealing the outcome of this claim:

Please Provide specific details and documentation to support your position:

This is where I need some assistance because it's not too late for me to fight back. Do I have a leg to stand on to appeal their conclusion? I unfortunately don't have proof that the damage was due to their improper use of the ball joint skate (I should've taken more photos but hindsight is 20/20) but the timeline between the photos I do have still tell a story. Between transporting my car to my mechanic and my car getting looked at by my mechanic, my transmission got cracked open. What are my options and do you have any advice on how I should answer those prompts? Anyone who knows anything about cars or law would be helpful too. I can also try to answer any additional questions you all might have regarding my situation. At this point, I just want this nightmare to be over and to finally have my car back.