Sounds like a great trip! For tire sizes, you *should* be fine with a stock suspension. I had 285/65/18 on my 2011 LC before a lift, and it only had minor rubbing on some of the plastic fender trim pieces in full lock/tuck scenarios (i.e. not that frequent to be overly concerned IMO). You can run some numbers here -
Tire Size Comparison and get a sense for fitment of various tire sizes, plus check out the
tire size database.
For your storage needs, have you considered a
hitch mount solution? (lots of options, just linking a list of suggestions for you to browse) Just thinking about all the highway miles you'll be logging, plus the occasional fast food drive through, hotel garage parking scenarios, etc. having limited clearance - not to mention fuel economy! Having your cargo tucked in behind you, vs overhead, will definitely help with MPG. I bought a cheap option from Amazon and it has the PVC coated duffle bag that holds a ton of gear!
Edit: I also have the Yakima Sky Box 21 for the roof which I use for skis, snowboards, etc. and it also works great. But if I had to drive a lot of miles and get away with the hitch mounted option, I would definitely do that.