The issue here is that compensation is both the wrong thought process and the wrong term. You also need to separate out perceived service shortcomings from actual damages you suffered. The former are about a customer service gesture and that is what AA gave you. Whether it is sufficient is a matter of opinion.

As this was an international flight, the Montreal Convention applies and you are due the fair market value of he scooter or what it cost you to fix it. It is unclear that you are due consequential costs such as paying someone to meet you, but I doubt that AA will quibble.

You should submit to AA a short and concise statement which focuses only on relevant detail. The exact nature of your disability is not relevant nor is it anything you need to discuss with AA. I would also leave out all of the who said what and your assessment of the law relating to the return of disability equipment.

Thus:
1. Checked in a scooter for gate return at JFK.
2. It was working when checked.
3. It was not working when returned due to damage.
4. Incurred the following expenses:
- Repair of the scooter (I realize that this may be $0, but you ought to then simply point out that the technician repaired it without cost to you)
- Payment for special assistance at home. Provide a receipt, even if handwritten and a copy of the cancelled check.

It may well be that the $350 voucher is a much better result than the cash you would receive for your out-of-pocket expense to the person who assisted you. Whether it covers the entire cost of a ticket, it defrays the cost by that amount and has value if you intend to travel. But, it really is your choice.

While I realize that you replied above that you do not own, but rather rent, I do not believe that the suggestion was confined to homeowner's insurance, but could include renter's, an umbrella policy and even various other policies.

Finally, remember that every carrier operating out of a US airport has a (Disability) Complaint Resolution Officer (CRO) available either in person or by phone during operating hours. While your initial request for a taxi voucher was properly made to an employee, presumably in the baggage area, if that was not promptly dealt with your immediate request should be for the employee to put you in touch with a CRO. At JFK, I presume that it will be someone physically present. CRO's are trained and can cut through other issues and also put you in touch with the right people to handle reimbursements (which is what you are looking for, not "compensation").

As someone with a disability, you should familiarize yourself with the CRO process as it may be helpful in any respect where there are disability-related issues.