How about if the Yoko tyre, seeing it's now a control tyre, was supplied as Medium compound to all competitors.
This would reduce the amount of sets required to be competitive so saving $$ for competitors and increase the laps required to get them into the go zone.
This will/should put an end to the 1 lap wonders. (I understand Time Attack is about the fastest lap, but that doesn't mean it has to be on the only lap done)
More laps for your buck is always a plus for me and will be a plus for the event/sponsors/spectators.
They could be marked in a way, similar to the yellow stripe on the soft supertaxi slicks so it's clear your running the control tyre to the scrutineers.
Any entrant caught not running this special marking is to be kicked out....? Clearly they are trying to run a softer compound if their tyres aren't marked!!
Just a thought, not perfect, but something similar might work.
You only have to mark the outside of the tyre so any sets left over after WTAC could be simply mounted on the rim on the inside for future sales until all sold.
(I think the Yoko A050 is directional only and not left to right)