Having done a fair bit of tyre modelling over the years (and lap sim work in general) I can safely say that the hardest part of the car to quantify is the tyres.
When we put togethor our current tyre model, we really had to go back to first principles as even the most experienced tyre guy was of little help. The actual test rig data the tyre companies rely on is also flawed. I liken it to engine builders and dyno figures. Works for them in a relative sense but in absolute terms it struggles to track with reality.
Most of what you will read on the web is generally derived from Pacejka's work, which is fine for road cars but falls apart in the racing world, especially when it gets to the post peak slip angle regions. Racing tyres are also very temperature sensitive compared to road tyres, as you've probably already figured out.