I have the same tractor, I got it with the R4 tires and have owned it for almost 3 years now with no issues with the tires. As far as patching your existing tire, I feel it might work temporarily but I would replace it. If your just replacing one tire, get the exact same tire. If you're going with different tires, get all 4 to avoid issues with the 4wd.
How is the r4’s on the grass?