I've quartered logs, as this, before. Build a box, like a window planter box, with one side open and the inside measures slightly (1/16") larger than the diameter of the logs (not perfect cylinders). This is your sled. Attach the log to the box, at the ends, with screws in the three quardrants you will keep. Make two passes for each cut with the cut-away portion of the log on the opposite side of the blade as your fence, ie., your box will always be against the fence. Spin the box around and cut from the other end for your other cut, ie, your sled will, again, be against the fence. Multiple cuts, fast and easy. If the screw holes are an issue, carve some "dowels" from your scrap and drive them into the screw holes.
Sonny