I would switch to the 1 pm Alaska flight, or the United 1:37 pm flight, which are only 53/90 minutes earlier than the OP’s original plan. SFO has some pleasant ways to pass the extra time, including an aviation museum close to the International-A security entrance (where BA operates).

As others have noted, there are lots of potential problems with the current plan. AS might not be willing to check your bag through to Heathrow, and then you would find yourself having to wait for your bag at Concourse D, motor over to BA checkin at International-A, wait in line at checkin, and then wait in line at International-A security. All of this in peak season at SFO. Even if you’re okay rolling those dice, is your wife also game?