Bulge in the sidewall

Hey guys, this past weekend I was cleaning my quad and I noticed a bulge (about 1.5" diameter) in the sidewall of one of the rear tires. These are the stock tires on my ’15 Touring 1000. I’ve never been the type to buy aftermarket rims / tires unless it’s necessary (and now it is), so I don’t really know what’s what with regard to tire sizes / manufacturers / capability etc.

From my research, I’m leaning heavily toward a set of radial tires, and I want to go at least a size up from stock because I had some serious clearance issues on Drummond Island over memorial weekend (the kind of issues that required a crow bar to "adjust" clearance between the engine and the skid plate). It looks like a lot of people like the Bighorns, Bighorn 2.0’s, and the Bear Claws. From what I can tell, the Bear Claws only come in the 26" diameter for my 14" wheels, so those are out. I’m looking at the 29" Bighorn’s, and the 28" Bighorn 2.0’s. I don’t want to lift, or put a new clutch in the machine, but I’d like to gain as much ground clearance as possible since I have to get new tires anyway.

Anyone have any suggestions? 28" vs 29" pro’s & con’s?