It would have been easier if there was a "clip in system for the lines instead of having to thread them but figure it may be easier and better to dedicate a set of lines to this and just leave the whole rig set up with lines already threaded.
I found this cool double pulley that has swiveling side plates that will eliminate having to thread each line through the pulleys.
I totally understand the "heat" thing... There is low heat shrink tube and as long as you use a hair dryer it should be fine. However; please try this at your own risk and practice on some scrap line to get the feel for the tubing. I am attaching some before and after pictures.