However, you still have to state this in a way the court will accept. You may consider hiring a paralegal if you have no experience in this, especially consider the seriousness of a careless ticket....
Also, will the court expect me to send a second request? Does that even make sense a week before the trial?
I checked a little more into my previous situation, and I received the notice of trail May 2nd or 3rd, but the date on the notice said it was issued April 19. In any case, my paralegal filed for disclosure within a few days after that, and my court date was on July 7th. The courts gave us the disclosure two days before the 7th (which would be the 5th), and we used this to file a successful 11b.
I'm almost certain that you have to give the courts either two or four weeks notice. Eight weeks doesn't ring any bells in my head. At any rate, like you say, you couldn't of filed for disclosure any earlier than you did (give or take a day or two), so, provided you have a time/date stamped proof of when you first filed for it, you should be golden. Just keep checking with the courts during the following week to make sure whether or not they have it ready.
Just make sure, if you move to adjourn the trial, make sure the courts put it down as them being at fault for it (failing to provide you with disclosure/failing to provide you with disclosure with adequate time to prepare a defence).