From a barrel racing perspective, I doubt collection is the same as defined in dressage. Your best bet may be to post the question on the barrel racing subforum.
I don't barrel race, and I don't do dressage - so take this FWIW. It may be close to a barrel racer's perspective:
For speed, I want the horse extending out. I want the weight to be carried by the front legs, while the rear legs provide the thrust. However, if you tried to go around a barrel like that (or a pylon when I'm practicing general riding), you'd get a huge, sweeping turn. Even if you slow the pace down, the horse can't turn efficiently.
So for a turn, you want the weight transferred more to the rear, and the horse to bend around with a light front end. For my riding, turning around pylons, I find I get a faster and more coordinated turn if I shift my weight back, tip the nose in a bit and try to keep the horse's inside shoulder up while the horse almost uses more of a swivel motion than a running motion. I'm not very good at explaining it, but I'm sure there are barrel racing videos, or perhaps your friends can demonstrate.
I did a lesson where I tried to have a horse turn a steady, tight and ROUND circle while I had my weight forward. Halfway thru the turn, I'd shift my weight back. It was obvious from feel that the latter gave the horse an easier and faster turn.
That isn't collection from a dressage perspective. Littauer argued in one of his books that a jumper almost never 'collects' in the true sense of the word, but does need to 'gather' for a short period of time. I don't jump either, so I'm just passing on some stuff I've read and some playing I've done for fun with my horses. Take it with a big grain of salt. Or two. Or more...