I believe the NT01 is the same compound as the Toyo 888. I used the 888's for half a season. What a terrible tire! Didn't last long, heat cycled out very quickly. You could tell when they got hot, as suddenly the track was covered with
oil. Based on that, I wouldn't want to use them as a street tire. 2-3 hours on the highway in July, and you've overheated them.
OTOH, now I'm using the 555's on the street. I like this tire. Excellent dry traction even when cold. Nice firm sidewall. I put them on last year, and so far the wear is excellent. I'd buy these again in a minute.
The 555R is meant for the drag strip. It's not a wrinkle tire, but the sidewall is much more pliable than the 555. It might give you a little smoother ride at the expense of some cornering ability. That shouldn't matter even in hard street driving. But it might matter in an emergency maneuver. Maybe just splitting hairs here, though.