Possible?
Why not cascade the responsibility for security to the local level? That is, to the airfield operators. As they are the ones usually handling radio comms and flight plan messages, they could establish a procedure based on their personal knowledge of the aircraft / aircraft owners / aircraft operators.
As some of the airspace is already in a TMZ, on a daily (or even hourly) basis, a unique squark code could be provided by higher authority to the airfields, who would only pass this on with the knowledge that they were accepting security responsibility in so doing. In addition, if necessary, this could be restricted to Mode S equipped aircraft, thereby enabling unique identification.