Got a tour in Heathrow on 23th May. Regarding the situation and the previsible content of the update, I called them and booked a tour just telling them that I was on Stage 3. Got an answer in 5 days. Got the 23th by chance. I've booked the 25th for Stage 3. I strongly recommend to you trying calling Heathrow, you are still on time.
regards and good luck for you all, fellows
Jessel