I suppose I'm a bit late to this, but in my experimentation I found (what I think anyway) is a better and simpler alternative.
Really, the thing about pulling back the BS is not the mechanical advantage, it's the progress capture that's important. I got tired of having a mini-traxion flailing around after I pulled the trigger, not to mention having to scavenge it to use for other stuff.
I started using a piece of 1" tubular webbing tied in a klemheist onto the pole. Slide it up, clip the shackle in, and pull down the BS pouch and webbing at the same time. The webbing will grab on the BS pole just like it would on a rope. It's very easy to get it all the way down to the bottom of the pole, no MA required.
I'd recommend making your own endless loop using a water knot so you can get the length exactly right (for maximum pull) and having the release shackle inside the loop.
Hope this helps.