I spoke to a couple of people on the CTT London South district committee last night, and gleaned the following: Neither Box Hill or Tilburstow Hill are currently approved CTT hill climb courses, so that pretty much rules them out for this year at least. Ranmore Common Road is an approved course and is only a stones throw from Box Hill, so would be a good alternative. The suggested date of Saturday 30th September is OK, as there are no other events scheduled for that day.
If people still want to do Box Hill then it could be done as a BC event (as per the 3-day Rob mentioned) rather than a CTT event, although that might bring other complications such as the requirement for race licences etc.
Or "The Third Way"; people can just time themselves as they ride it, and have it as a completely unofficial "non-race".