I don't think N3's have enough grip, I use them for drifting all the time because of how little they have, only just enough for some control while drifting, not suitable for actual speeds.
No disrespect intended here, but I think you may be too accustomed to video game speeds rather than realistic speeds for these stock cars. I feel the N3 tires really give these cars the level of grip they'd have off the showroom floor with factory tires, and despite the lack of analog controls, they provide a very good sense of the cars' actual handling characteristics. The IS200 is a perfect example; if you brake too hard and transfer a ton of weight to the front while turning in, and get on the throttle hard before allowing the car to settle, you'll have your hands full of opposite lock. However, if you brake early, release the brakes, turn in gently (tap-tap-tap-hold to full lock if you're using the d-pad), wait until the car's weight is a bit more settled and you've got the apex lined up, THEN gently get on the power (tap-tap-tap-hold to full throttle) while allowing the front wheels to slowly come back to center (which again may require some tapping in the direction of the corner if you're using the d-pad to slow the front wheel's automatic re-centering), you'll find that it sticks and goes with very little oversteer, just like it should.
The biggest drawback is the lack of analog controls. But with some patience and practice, you can effectively overcome it.
Also, one little trick I've found is that it's very helpful to pay attention to the speedometer while you're exiting corners when you first begin putting a car around a certain track. See, in a real car, spinning the tires causes the speedometer to jump up and report a speed faster than you're actually moving. In the game, however, the speedometer always accurately reports the speed of the car itself--i.e. it's not based on the speed of the tires' rotation. So when you're spinning the tires while exiting a corner and losing or maintaining momentum rather than accelerating, the speedo will actually show the drop in speed or the maintained speed. You may not be able to hear the tires slipping in-game, but if you're holding the throttle on a corner exit and gaining no speed, you can rest assured you've exceeded the tires' limits of grip. A couple of corners like that can take tenths off of a good lap, and it's sometimes hard to notice, especially if you're only exceeding the limits of the tire by a fraction of a percent. The Miata/Trial Mountain challenge from Season 2 was the perfect showcase of this effect. So keep an eye on the speedometer and learn how much you can push the cars before you cross that peak of handling performance and begin losing or maintaining your speed instead of cleanly accelerating out of a corner. This will help drop your lap times significantly, and will help what you may have thought to be an awful car become much more predictable and enjoyable.
I realize this was a bit long and ramble-ish, but I hope it helps you guys who may feel the N3 tires aren't grippy enough. If that's the way you feel, I'd be willing to bet serious cash that you're just trying to take the corners at unreasonable speeds. If you nail a corner perfectly on N3s, take a look at your replay. Looks very realistic, eh?
Edit:
I'm diggin' the N3 tires... they add a new level of challenge and realism to the competition.
I tried out the two Lexus IS 200's last night for a bit. The stock one is a real pain to keep on the tarmac. It will take a bit of time to learn at just what speeds it can handle certain turns.
Basically read my mind. 👍