That is a serious machine, I'm sure it was hell on your lawn with R1's! It'll be interesting to see how these do, I've never seen anyone run them around here. Most here have been doing R4's the last 10 years, although enough people are seeing the downsides to those, that now they're starting to try other options.
I just run turf tires, and chain up on very rare occasions (less than once per year) that mud or snow require it. HD chains for bulbous wide 41" tires are heavy and expensive, and I really hate them, but they give me instant four corners of R1 traction without playing hell on the lawn the rest of the year. Finding heavy front turfs for maximizing loader capacity is always an issue, but the options are out there, if you hunt for them.
Turf tires actually do remarkably well plowing snow on asphalt, they just clog up too easily when pulling the wood wagon across a snowy yard. If the wood wagon is getting low (every 3rd week), and there's a big snow in the forecast, I try to get it filled before the snow comes to avoid having to drag the chains out. I try to time any ventures into the wetter and muddier parts of our woods for dryer (or frozen) times of the year, for the same reason.
Those TRI2's are more akin to turfs than an R1, with a slightly more aggressive tread and much harder shoulder on the tread. I'd guess they share at least some of the same advantages and disadvantages.