Get new galvinized wire rope. You really do not want stretch in the winch cable. if you're geting fish hooks, it's time for new. Wire rope is also easier to unfoul if you get a turn crossed.
Standard cargo gear safety factor, whether lifting or pulling, is 5 to 1. You'll not really even need that as you shouldn't be straining with the full weight of the boat. Yet you want something strong enough to keep your bow eye chockablock to the winch, not parting, if you hit a whoop-de-doo going down the road. I'm not in favor of something that stretches in that application.
“Scientists are people who build the Brooklyn Bridge and then buy it.”
Wm. F. Buckley, Jr.