I'd be pissed if the girls used our high-bar as a strap bar. Totally unsafe in my opinion. We generally just spray the bar with water, then apply lots of chalk. Works for the most part.
If you're naturally a left twister, twist left, if you're right, twist right. Most kids learn a cartwheel/roundoff without first determining their twisting dominance. So I wouldn't take that into consideration as to which way you should twist.
Then there are the odd kids who can twist just as...
I'd also recommend not using your round-off to decide which direction to twist your barani, since a round-off isn't really a twisting skill. Learn you twisting dominance by doing lots of easy skills on a trampoline like swivel hips, rollers, cradles, cruises and so on. If you then determine you...
A big part of the job can just be trying to promote boys gymnastics. Making sure you get results into the local newspapers, planning demonstrations, stuff like that.
One of my biggest challenges is just trying to integrate our boys program alongside the uptight women's program in our gym.
That's not a full twist in the video you linked to. You start twisting right, and then twist to the left. I'm guessing you're a left twister but your barani is messed and twists to the right. A common mistake. You should definitely determine your twisting dominance and then go from there...