I've not shot any competitive skating, but I've strobed a lot of hockey. I don't like the look of direct strobes, and only do this as a last resort (when the arena lighting is so bright that I can't stay 3 stops or more above it with my bounced light), so I bounce mostly, my lighting is pretty spread out. However, unless you use Speedotrons spread all over the ice, you're gonna have a bit of variability in your lighting.
I'd place your three lights behind you on light stands, and shoot from center ice. Put one light around each face off circle and one behind you at the center line. In this case, if you have the sports reflectors, I wouldn't use them, as you want your lights to be wider angle.
The third (and holding) episode of the podcast in my signature gives some info on strobing.