Go to
www.ba.com, Executive Club, Spending Miles.
Then hit "Book travel". Enter your locations and dates and they will show what is available on BA. Print it out and circle your best options.
Then call AA and tell them the flights you want them to book for you. Pretty straightforward. Yes, it seems intimidating. I remember the first time for me- I booked BA First Class with Cathay Pacific miles since at the time, Cathay wanted 90,000 miles for the same seat that BA wanted 150,000 for! But it is really pretty easy - especially if you are telling them exactly what you want booked (and since you already checked, you know it's available).
NOTE - no matter what the BA website says, in terms of miles, it will be according to the AA schedule.
In terms of fees when booking thru BA, I agree that the fees are high but it is the price I am willing to pay for great availability - especially for First Class travel! $700 is way less than a coach ticket and I get to go First? No deal-killer as far as I'm concerned!