I agree that the snowshoe lace or rawhide with varnish is a nice rustic look and bound to be very durable. It breathes well and doesn't hold moisture.
I have used paracord for lacing the seat on a drift boat which was very comfortable, breathed well and did not hold moisture. Traditionally on a drift boat the rope seat is only woven in one direction across the beam.
Thanks for the reply's, I have the black webbing but was on the fence about using it or cane. I'll go with the webbing. I removed the old cane yesterday, sanded the frames and slider frame, then coated them with varnish.
The old underside of the seat frames will now be the new topside of the seats with this black inch and a half webbing.