If you do decide to switch, think carefully about the timing. First try to qualify for elite status with AA by the end of this year. Then assess whether you want to continue with AA for 2015 (maybe earning the AA miles for the trip home in 2015 rather than by the end of 2014). If you do decide to switch, note that status matches/challenges done early in the calendar year often are good only for that year, while those done in summer or later cover the rest of that calendar year and all of the following calendar year.

However, for BA (and many other foreign FF programs) the program year is based on when you join (and maybe when you achieve status), not January 1 for most people to achieve status.

Your new employer might be able to get a courtesy status "match" for you with BA since it seems to have a BA contract and require BA tickets for your business travel.