Don't know about the 1006, but check your wheel well clearance. I had rub marks on the inside of the tubs from the OEM tires hitting at full suspension compression already. Adding an inch probably would not have been possible, although you could put taller travel limiters (bump stops) on the axle to prevent this rubbing.
My Kenda's wore better than the Carlisle's I eventually replaced them with, but many on this forum really like the Carlisle if you are looking for brand options.
Going to 13's does give you the option of radial tires (never found a 12" radial, they are all bias ply apparently). Just try to find one with an overall diameter as close as possible to your current outfit. For instance the Maxxis 175/80R13 has an overall diameter of 24.1". How does that compare to the diameter of your current tire?
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2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2018 Nissan Titan Midnight Ed.
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