WoW!! Congratulations!!!
All I know is what happened to me, pretty similar to what happened to you. I got the SSI backpay and medicare within 90 days, but the SSDI took much longer.
I got the fully favorable in Sept 07 and finally got the SSDI backpay in june 08. From what I understand the SSI causes the SSDI to be delayed as it goes through the computation process, and they also deduct the amout you got from SSI out of the SSDI backpay.
Hopefully yours comes in faster than mine did
Glad to hear you won.