....on making it look original, but still want a somewhat traditional look - you could use poly cord and do a laced seat like those on Nova Craft canoes. Or you could do it with boot-lacing like those on Merrimack and Navarro canoes. I prefer both of those to caning or webbing. You get a more traditional look (than webbing), great comfort (also dries fast), and the better durability. Plus - if you use a lacing pattern that is a bit dense, you even have an emergency supply of cordage that can be raided in a pinch.
natural vs. plastic cane? The natural cane on my 1992 Malecite is still comfortable, looks good, and serves well. The book “Building a Strip Canoe” recommends using plastic cane instead of natural. Does anyone have any experience with or opinions on plastic vs. natural for seat caning?
You’ve never had lawn chair web fail? Isn’t it nylon web? I’ve had the webbing on several of those fail while sitting in them. Maybe they were abused with too much UV - left out in the sun when not used.
Lawn chairs… …typically use the cheapest webbing. I don’t know the material, but it isn’t even close to the quality of webbing I see on canoe seats. And then it sits in the sun, day in and day out, for a few years before it fails.