I found the little red doohickey that comes with a reverb invaluable. Attach to a lenght of cable, in the hole at bottom of seat tube, out the top, attach to the cable for your new dropper, pull through – bassically allows you to go in the smaller hole and out the big one (steady) and then pull your new cable through.
Your down tube might be a little more fiddly – an inner cable in from the top and out from the bottom is easier than a full width cable, you can run it inside the tube, then reach in and hook it with a bent spoke or similar. Once that’s in place, you can use it to guide an outer, then us the method above again.