but there is clearly a significant issue here which I hope no other students will have to suffer.
What exactly are you missing out on DS3? I too had to wait a couple of weeks to get my paperwork together before I took it to the CAA myself. I then had to wait about three weeks for the licence to arrive. Meanwhile I continued to do as I had before - went flying with my instructor and did a few solos with the agreement of one of the available instructors on the field. Yes it is a bit of a pain having to wait for the licence but it will be worth it. I learnt a long time ago that what is important and urgent to me, almost is certainly not as important to someone dealing with a host of other things.