One solution I came up for this problem: Take you're rod apart and attach only the first section to the reel you need to reverse the line on, if you have someone who can this method works well with a second person but I've done it by myself as well. If you have a big lawn this method should work, if not go to a park or somewhere their is a vast expanse of grass and simply thread the line through the first and eye secure the rod and reel(picnic table, tree, etc. or better a friend holding it)pull off the line and backing in one fail swoop in a straight line or if needed double back. If you have a partner have them hold tension on the line as you reel it back on the reel right handed for left handed casting; If not try to create a little tension by placing a heavy bag on the line in sections, don't harm the fly line though. Also as you proceed make sure you have good knots from the reel to the backing and the backing to the fly line. You can find the info for the knot's on this forum.
Almost forgot, you will need to switch the reel on the seat and re rout the backing after you pull the line off : If you hold the rod in you're left hand you will retrieve(reel) with you're right.