Selecting an MCE seat in the Economy cabin on an AA nonstop would likely be the cheapest way of getting decent seat pitch on the flight. Technically, this is not considered an "upgrade," as you'd still be traveling in the Economy cabin. Moving from Economy to Premium Economy would be considered an upgrade.

MCE seats can be paid for with either cash or AAdvantage miles.

When you book, just make sure that you do not inadvertently book the BA nonstop under the AA codeshare flight number; no MCE seats on BA.