Semi-rigid tire bands for traction?

I apologize if this has already been discussed but I could not figure out any search terms here or on Google that led me to any information relating to what I'm thinking about.

I have an old MTD built Montgomery Ward lawn tractor that takes 20x8-8 tires. The tires on it are shot. They don't hold air for more than a few minutes and are very very dry rotted. I hope to use this as a "garden tractor" rather than a lawn mower so I am thinking about how to get the best traction out of it without too much weight reduction from my wallet when replacing the tires.

I found some 20x10-8 Carlisle Super Lug tires that I really dig the look of but the cheapest price I can find is ≈$150/pair and [although they are tubeless] I believe I still need another $30 worth of tubes if I want to use my stock rims. I couldn't really find any other comparable "lug" type tires in the ≈20" diameter for an 8" rim (other suggestions always welcome). This got me to thinking about other ways to improve tire traction while buying less expensive traditional lawn-type tires. Of course there is always tire chains but even looking at used ones on craigslist they still seem really expensive (>$40 for a rusty old pair, ≈$70 new).

My idea is to make something similar to tire chains but more rigid and a lot cheaper. I'd like to bend strips of 3/4" steel flat stock and weld it into circles that are ever-so-slightly smaller than the outside diameter of the fully inflated tire. Outside each rear tire I would connect 2 of these circles with strips of 1/2" flat stock or possibly even something like 1/4" or 3/8" round stock as "tread". I could even go all out and bend the round stock into V shapes to really dig in. I think if I get the sizing right on the rings, I could deflate the tire, slip these steel bands with the steel tread over them, then re-inflate. The pressure of the tires should hold the steel bands in place.

I estimate only needing ≈$10 worth of materials to make something like this and my time is free since I enjoy playing with my tools. The only real problems I could see with it were the steel bands fatiguing from constantly flexing under the tires or that I may be overestimating the amount of traction that steel tread would buy me. I assume that tire chains are so popular because the chain portion can bend and flex under the flat part of the bottom of the tire and does not wear out the way a rigid structure would.

I understand that many of you will read this and think "even if it works it still won't be any better than store-bought tire chains" and I can admit you are probably right but I'd still like to hear the thoughts of others on the pros or cons of a setup like this.