the one thing very helpful for me when I was learning was to swing the leg over and grab the tt very early and coast like that up to the barriers. If you have a straight run, it's not any slower - you just need the brakes less and often can hit the barriers at greater speed because you're focused and under control.
so regardless of unclipping first or stepping through, all you need to then do is get off the bike and pick it up. it's helpful to just practice coasting around holding the top tube. once you put some weight on that top tube hand, you'll find you're very stable and under control. then, over time, you can reduce the space/time you're coasting on the side of the bike. I find most new racers swing their leg over too late and get off too early on a set of high speed barriers (which are going extinct it seems).
One more thing to add...back when I was a junior and we could have LOTS of barriers (ah...the good old days) I practiced by making a set of 18" tall break away barriers by making upside down "T's" out of 2" x 4"'s and resting a 2" x 2" wooden bar on top. That way if I smoked it I wouldn't really hurt anything, plus it gave me the confidence to move into the barriers quickly.
I have to admit, after my hiatus from cycling during College I was pretty disappointed about the barrier rule change, but that is another topic.