I also remember reading something about Cortland gets tighter and stronger if it gets wet. I wonder if getting it wet would help preserve it. I'd have to look into it more, again, but that rings a bell.
It's funny you mention getting the linen wet. I can turn an average piece of green spot linen to look and feel like Cortland by getting it a bit wet. Never soaking it, as there's glue underneath the wrap. I make a solution of one part bleach to ten parts of warm water, wring out a wash cloth, and go over the wrap, time after time, letting it dry completely each time, never soaking it. When I think I've got the look down, then there's the finishing. Some wraps respond fine to just a glass rod rub, others need extra fine sandpaper to finish it off.
But Cortland, I don't think I would ever put any water on it. I would just make sure to get my hands on it, play it now and then.
I also wouldn't get an old spool of Cortland wet. If it's really old, it's dry rot, and no amount of water will bring it to life.