Sorry no idea on recycling but it has occurred to me in the past, usually whilst cutting old and battered ropes down and observing how pristine the core is(or at least appears), that a rope 're-sheathing' service might be a good idea. Probably in a minority of one here but I'll press on....a core is typically made up of 10 or so main strands. These strands are themselves made up of 3 thinner threads that are braided together. My guess is if you unbraid all the threads, replace ~25% (?) of them with new for peace of mind then braid 'em all back together and whack on a new sheath you'll have a rope that handles, performs and tests as new. For further peace of mind, you could easily destructively test one of the old strands that was being replaced to check (infer) that they're all still good.
On a similar note if manufactures made just the first and last 3 meters or so of a sport rope sheath much more hardwearing by augmenting with something like kevlar, heat/dirt/water/resistance treating, beefing up the the sheath weave count, etc. a sport rope would last and remain full length for so much longer. A cynic might wonder if manufacturers might want their ropes to wear reasonably quickly.....
