I use the 20 Gallon Brute and I only move it empty. I put my fermentation fridge up on stilts that I built out of 4x4s and on old pallet. I pump my wort directly into it from the kettle (via the counterflow chiller).
I drilled a hole near the bottom and put in a bucket spigot with a PVC 90 on the inside to use as a dip tube. When I'm ready to fill kegs, I spray the spigot full of StarSan from my trusty spray bottle, attach a sanitized hose, and gravity feed directly into kegs.
I use velcro to attach the temp sensor for the fridge to the side of the fermenter. Works great! I do hove to slide the fermenter a few inches forward when I hook up the hose, but no big deal.