Once tyres are cleaned and the rubber softened with some form of solvent the next problem becomes "dust" on the tyres...
As the tyres become more sticky they will pick up debris... So get out the Gaffer Tape and roll the rear tyres about 20cm along the sticky side and a black residue will be left behind along with any dust...
Repeat this process every 5-10 laps or so... what will happen is the loose muck and debris will be lifted from the track onto the tyres and onto the tape never to bother you again...
Once the track is clean you will see another second or so tumble off the lap times....