Slightly conflicting uses....road.....1/4...trackday
A tyre that will be good for the 1/4 ( what surface ? ) probably isnt going to last too well at a track day
And a bog standard road tyre, probably isnt going to be too hot...or indeed last long at a trackday either.
888's, and especially the new R888R are overpriced, and in big sizes...have little tread so mileage will be crap. I've jsut went through a set without even putting any real hard use on them. I was shocked at how little tread was on them at 275/40x18. Oddly..these had much less tread than the front 235/40x18's
TriAce, popular with drifters off sizes similar to what you ask and are quite a soft tyre, for fairly sensible money and decent tread depth and appearance. I've just put a set on the back of mine, although havent had much chance to use them. But were recommended by a drift friend, and he said they were very very grippy. And the ones I got, 285/35x18 ( 100 ) are pretty soft.
https://tri-acetyreseurope.com/shop/
I had Westlake Sport RS before the R888R's ( again, another popular drift tyre ) and I thought they were good too, only went for the R888R when I did as Westlake didnt have the size I wanted. I was really unimpressed with the Toyo though which was a surprise.
https://westlaketiremotorsportseurope.com/shop/
But many do also rate the likes of Micheln PS2 or whatever names/numbers they use now. Lets face it....they've been around for long enough with enough motorsport, they're tyres should be good.
That said, I did use a pair of Pilot Sport Cup's a few years back and they were absolutely lethal. Might have been great after 20 laps or so...but for road use or anything like it, they were like driving on ice.