One thing that concerns me is, in situations that would cause a winch to heat up, the steel cable wound on the drum would act as a heat sink, drawing heat build up away from the winch. Synthetic line would act as an insulator and may have been a contributing factor in Bill Burke's experience with the 1st wrap melting.
I use cord made with the same fibers as AmSteel and Technora all the time for climbing. The cord is spun and woven to give it different handling characteristics, but the physical properties are the same. Let me share a few experiences both good and bad.
Technora is tuff stuff. Very heat, abrasion and cut resistant. So much so I ruined a new Spydaco knife trying to cut some into usable lengths. It won't melt, you can't burn it with a lighter or melt it with a soldering iron, to singe the end to keep it from fraying. You have to dip the ends in epoxy. Technora will hold a knot. The problem with it is, it does not like to be bent over acute angles under tension. The fibers are fragile and repeatedly running it over, say a fair lead, at an extreme angle will damage it. I use High Tenacity Cord, a Technora product, tied in various size loops for rigging anchors. The manufacturer recommends that any knots that have been severely loaded be untied and retied in a different spot in the cord because the fibers that are tightly wound in the knot can be damaged and subsequent loading may cause failure.
Using a winch line made entirely of Technora would make me nervous, I wouldn't want to repeatedly run it through a snatch block. A line using Technora as the 1st wrap around the drum would be the way to go, just don't spool it out far enough where it might be bent around the fairlead, use an extension strap, and it will last a long time.
the UHMWPE, in all its different forms is weird stuff. When its relaxed it is hard to cut, but put it under tension and all you have to do is think the word knife and watch out!! Make sure you pad any rocks it runs over or use an rub guard. Under normal use it is rather abrasion resistant and as Mr Burke pointed out it only fuzzes or pills, under not so normal use its not resistant and can be deadly, I'll explain latter.
The stuff slipperier than snot on a door knob, it wont hold a knot, no matter how hard you try. Tie a knot in it and pull the knot will come undone. Climbing gear manufacturers that use this stuff to make webbing will only sell it in sewn loops.
As slick as this stuff is I have had it wear right through the anodized surface of a carabiner in a matter of seconds under body weight. If for some reason I was winching in and out with the rope running over the some spot on the fairlead, I'd be sure to check for damage.
During a climbing lesson an instructor did a demonstration that realy made a point. He fixed a Dyneema sling to an anchor, ran a cord through the loop and "sawed" the cord back and forth. In a matter of seconds the cord went right through the sling. The heat from the friction had made the frayed ends of the sling stiff and brittle. Not a situation I would expect when winching, but something that can and does happen every year killing climbers. When winching I will avoid potential friction points at all costs.
Mr. Miller's post on the low melting point of Derlin has me rethinking my choice of synthetic rollers. I can see a potential problem if for some reason the roller didn't roll and the line ran across the same spot. I'm thinking I'll wait till he comes out with Teflon ones.
Disclaimer, I'm not a chemical enginerd, these are just my real life experiences with products made of the same fibers in situations where my life depends in them.