I think you should be fine as you are set up. I plow with a Lo Boy with a fast hitch (more weight on the rear tires). With no chains on turf tires was pretty hard to work with, but lately I have been using loaded ag tires and that has been fine, without chains. I have chains here (not the 'good ones' like yours, those are up north) but have never really needed them.
Traction is good, but if the traction is too good you can break something on the Cub before you break traction.... I would rather spin a wheel than break the torque tube or plow.
Try it with just the chains, if they spin on the tire you could add bungees or something to hold them in place. I found that 9.5 turf tires are nearly identical to 8.3 ag tires, so if you ever get ag tires the same chains should work fine.
I am very jealous of your shop. The rule seems to be, no matter how big it is, eventually it ain't big enough. Really nice! As are the Cubs!
1971 Cub (Rufus) 1950 Cub (Cathy) 1965 Lo Boy Fast Hitch (Nameless III) 1970 Cub 1000 Loader & Fast Hitch (Lee)