a few of our guys in the Roadgoing classes have used T1-Rs for sprints/hillclimbs and found them pretty good to be honest. They do, like most tyres with a reasonably low treadwear indicator rating, suffer from overheating if given death! once the surface is overheated the oils dissapear and the surface hardens appreciably. The only way to get rid of this is to remove a couple of mm of tread depth. this must be done without heat, i.e. natural wear due to normal driving road miles, or have the tyres 'shaved' my a motorsport team. the difference is huge.
some tyres, not sure about the Toyos, have different shore hardnesses or rubber throughout the tread block depth. The first few mm are harder as the tread blocks move around more when new and full depth, creating more temp in the block. when the tyres become worn down to near the tread wear indicator bars, the rubbers softer to compensate. Thats why a lot of racers that have tio run road tyres buy brand new tyres and shave 5mm of tread off before running them

the rubber also ages too. If the tyres are a couple of years old and yet barely used, they still wont be market fresh. Heat/cold cycles and UV light affect the aging hugely.
Tyres that have seen a lot of arc/mig/tig welding (ie stored in a workshop where lots of weldings done) will age the surfaces that are exposed. On a std road tyre the effect isnt as bad as on racier rubber (R888s, Yoko AO48Rs etc and especially slicks/wets) but still will affect the tyres performance markedly.