Often1

Filing a fraudulent chargeback is a very, very bad idea. Especially when you've just lost your job and do not want anything happening which might jeopardize your access to credit (you may need it). You bought the tickets, you agreed to the fare rules and you owe the money. Whether your former employer owes you money is a different issue, but has nothing to do with AA/US.

You may also need to ask your CC issuer to forbear on collections if you are having a tough time. Attempting chargebacks -- which are expensive for the CC issuer -- is not a way to put them in a mood to help.

You also will have your "appeal" within AA fall on a lot more deaf ears when the chargeback is logged. From AA's perspective, they did nothing wrong.

First and foremost, you absolutely need to consult an attorney. As I read it, you have at least one paycheck, some other unreimbursed expenses and these two tickets at stake. I realize that times are tight, but spending a bit to preserve your rights may be critical. Some of your coworkers may be in the same situation and perhaps you can do a joint consultation.

Sounds as though your employer is in some form of bankruptcy or will be very soon. If they have shut down, their commercial creditors will force the bankruptcy anyway. You may have a priority and there may be some assets to pay you. But, that won't last long. All DOL can do is monitor to make sure that assets aren't sold until employees have been paid wages due.

ADDING: Just occured to me that your travel insurance (or your employer's, may include loss of job as part of the coverage. Check that quickly. If so, no need to do anything other than collect on these two tickets).