I had two flights that I cancelled and I had to complete the application for refund 2x. The refunds were processed in about 6 days. Both were credited back to the original card.

I had a ticket that I paid for for with a $ 500 voucher and $390 cash total $890 First Class JFK to Bogota Colombia connecting through MIA.

AA unilaterally changed the departure time by 3 1/2 hours later and ending in MIA. on departure. Of course I cancelled and put in for a refund.

Though AA refunded me the $390 cash they had the balls to charge me $ 173 on the voucher for changing the flight. In other words giving me back a
$ 327 voucher vs the full $500.

I put in a DOT complaint which AA has 30 days to respond to which they now have 7 days left.

Applied for refund on 4th April. It was finally approved on the 11th May.

Complaining after less that a week - like the OP - is really unreasonable at the current time. Don't care what the DoT policy is they aren't fining any airline for not meeting the 7 days are they?

I made a complaint to the DoT on 4th May and no response from them

Credit Card may be an option but when I called mine (MBNA in the UK) about a long delayed Finnair refund that was well over due they told me it was takign 45 days for them to start to look at them such was the backlog they had.