I've been using shielded 10/24 stranded for drop cable, but it sounds like you could use 8/24 since you're only using four pair on the mountain's comm cable. As you mention, that comm line is AWG 24 so you won't see a meaningful increase in resistance by using the same gauge for drop line.
Stranded is much better for repeat use than solid core like cat 5. That won't roll up again for re use without great difficulty.
Good quality terminations and storage are as important as the wire you use. Fred's picture of the reel shows the way to do it (although I'm not a fan of the Hirschmann plugs for outside use, that tiny set screw is not very winter-friendly). I like to put the plugs into a ziploc freezer bag taped shut when reeling up, prevents banana plugs from being yanked off as the cable is dragged through the snow.