The nicer the surface, the higher the psi. In ideal conditions (say a perfectly smooth roller) higher psi will be faster than lower psi. The problem comes from imperfections in the road/track surface... at lower psi the tyre deforms around the imperfection, at higher psi it bounces. So at Carson say, which is wood and *pretty* smooth, you can run higher psi than you could at somewhere like Rock Hill, which is paved and not especially smooth. The worse the track surface, the closer to "road psi" you want to get, but for the most part, it will still be higher than what you'd run on the road.
As for clincher vs. tubular... plenty of people ride clinchers without issue. The problem is when things go tits up and you flat on a clincher vs. tubular, say at speed... on a (well glued, which is another issue) tubular you've got a shot at riding it out with the tyre still on the rim. On a clincher you're just SoL, that tyre is coming off and you're going down. I did that last year riding my Trispoke... full speed into turn 1, tube blows and I skate with the rim into the turn, then gracelessly take the slide of shame (and pain) - would I have been able to save it on a tubular? Maybe not, but I'd have had a shot.
(fwiw you also cannot inflate a clincher to high'er' psi's if you ever wanted to)