I got the AA miles back right away and the BA taxes back within a week for the flights booked with AA.
I'm still waiting to call BA for sometime when I feel like sitting by the phone while I'm on hold. Wish they'd call you back like AA and UA do.
The flights aren't until the end of September, from Prague, and end of November, from Delhi, so I've got plenty of time to hope BA restaffs their customer service lines. It would be nice to get the taxes back but I'm not in any hurry to use the redeposited Avios.
