The SPG Amex points post as soon as you hit the £1,500 (in my case, 3 days after activating the card!). They go to Starwood at the end of the statement period and you can then transfer to BA. You should have the 15k within 7 weeks - 10 days to get the card, 4 week statement period to spend the £1500 (buy a refundable BA ticket if necessary and cancel it next month) and 10 days for the SPG transfer to go through.