FWIW, the following worked. I faxed this to them and UA responded by email 10 days later. They upped me from General Member to Premier Exec, expiring in 2/08. I had 16,951 YTD EQMs on the AA statement I sent, dated 6/26/06.:

Date: June 26, 2006

Number of pages including this cover: 2

To: UA Mileage Plus Service Center
Premier Service Match

Fax number: 605-343-0215

From: ORDinary Gold, Mileage Plus # 99999999999


Message:

As you can see from my attached statement, I am currently have “Platinum” status on American Airlines, but I would like to shift my business to United. I have a trip booked on UA for tomorrow (conf # X9X9XX), and a number of additional trips in the works, which I would prefer to fly on UA if you would be willing to match my elite status to your equivalent level.

Please feel free to call me at 999-999-9999 or email if you have any questions.

My Mileage Plus number is 99999999999.

Thanks in advance for your consideration.