Timed events do not have a race category associated with them since you are on the track by yourself unless the promoters decide to do otherwise so checking is appropriate. I looked at the flyer and did not see a 2K pursuit for men at NTC. They offered 200, 500, Kilo, 3K and 4K for men. The women were offered 2K. You could race with them.
I raced at T-Town and it is a fun track but it was hot and humid.
You will have no problem on the 333 versus the 160. You turn less on the 333 and power is on all the time. It will be good to practice pacing to get your lap times and gearing dialed in.
Whatever you can do, or dream you can, begin it. Boldness has genius, power and magic in it. - Johann Wolfgang von Goethe, writer