I give myself a little extra wire when stripping the outer sheath. After that, I bend them all outward from each other, at a 45-90 degree angle and untwist the pairs. Then I bend them back, get the wires in the right order, and straighten them out just enough to push them into the RJ45 connector. After that, I push them into the connector a couple times to finish straightening them out. Then I trim them to the right length, push them in one last time, and make sure I can see the shiny ends flush with the plastic when I look through the end of the connector, and finally I crimp the connector.
It doesn't take many cables' worth of untwisting to kill your fingertips! In the past, when I've had to unwind about 10' of twisted pair for hobby projects, I stuck the end of the wire in an electric drill and tightened the chuck. Then I just pulled the drill's trigger until the pair was unwound. If you could figure out a good way to quickly clamp and release the pairs, you could do the same with an electric screwdriver to untwist the small amounts of wire needed for putting an end on.