I am the original poster. Here is the chronology of the EC 261 compensation process. This supplements the information contained in post #13 of this thread.

Saturday, May 24: I submitted the e-mail request for EC 261 compensation to the AA.ECClaims address. This was the Saturday of the Memorial Day weekend.

Monday, May 26; Even though it had been a holiday weekend, and Monday was the Memorial Day holiday, I received an e-mail with an offer of a 600 Euros refund. I was asked to provide my mailing address since claimants who are residents of the United States or Canada would receive a check in the mail in United States dollars. Residents of other countries would have the funds transferred to a bank account. Within two hours I replied by e-mail, submitting my mailing address. I made no claim for out of pocket expenses.

Tuesday, May 27: I received an e-mail promising me that a check would issue in the United States dollar equivalent to 600 Euros. I was told to allow 45 days for delivery. A check was issued on that date.

Thursday, May 29: An envelope containing the check was metered with this date.

Tuesday, June 3: The check was received by standard mail.

I should add that every e-mail, and even the bottom half of the document which contained the check, included an apology from American Airlines and a plea to travel with them again.

I wish to thank Mr. BoH and the other posters on this thread who assisted me throughout this process.