Your best bet for reverse bleeding, given the condition of the fluid in the system, is to suck fluid out of the reservoir so that it is below the level of the clutch nipple. Then remove the hose from the reservoir nipple. Connect a piece of hose to it somehow and run that hose into a drain pan.

THEN do your bottom up flushing and do it THOROUGHLY. This way you don't flush dirty fluid into the brake reservoir. When done, reconnect the hose at the reservoir nipple and fill the reservoir. The little bit of air that will be in the hose from disconnecting the drain line will easily rise into the reservoir in the form of bubbles.

Good luck,