Without knowing everything about your set up including your arrow spine and draw weight its hard to determine what your problem is. Out of a properly tuned bow your FTs and BHs should hit the same point of impact. Sometimes just a minor move (1/32" or less) of the rest could be all it takes to get your BHs shooting tighter groups. Sometimes if your arrow is under spined slightly there may be no improving your BH groups. Which direction did you have to move your sights to get your BHs on target?
(example: if your BHs were hitting left of your FTs you would have had to move your sights to the left. I would bet now if you shot your FTs they would hit right of the bull. If so, move your rest in ever so slightly and shoot one BH and one FT and see if there was any change. Note when you move your rest, your FTs will also change POI but not as much as your BHs. You will reach a point when they will both hit the same or very close to each other. Then adjust your sights accordingly. If not then you likely have a spine issue.)
But you're right about the Whisker Biscuit. My suggestion would be to get another rest. Preferably a drop away.