Mode S will rule out a lot of older aircraft, but regardless of that, it's not the machine that the authorities are worried about, it's the unauthorised use of those machines. A special 'Olympics squawk' will last 5 minutes, before it's leaked and the whole system is compromised.
There's plenty of time, so I'd recommend a proposal from one of the 'invited few', based on detailed applications NOW from the specific pilots who will be affected. This has to be in the form of unique codes allocated and sent to the home addres of each security-vetted individual, who will be asked to quote randomly selected characters from their own unique code on lifting. There could even be a special sequence of characters that would indicate a '7500' (unlawful interference) situation.
As I've said before, if someone wants to fly into Buckingham Palace, Houses of Parliament, etc. there ain't nobody gonna stop 'em, but the current proposal paralyses the industry and prevents spontaneous private activity in the Restricted Area quite unnecessarily.