I had a similar scenario. I sent out my 5 letters via my schools service to AADSAS and then got another letter (my final letter) and sent that to addsas it took about 5 weeks for my last letter to join the other six. It maybe due to the huge load they had in August.
DesiDentist
PS: I would try to send your last letter to the schools seperatly to facilitate the process. Some schools are already booked until april, it might speed it up a lot.