First of all, where are you living now? And when are you planning on coming this way? (I live in Tillamook!)
Because, like said in earlier posts, for traveling across the country loaded with everything you own, its gonna be a slow and sluggish drive, when your are not in the flats. You are gonna hate the long steep climbs. Your gonna be stuck with the truckers in the SLOW lane. So, what I would do, if I were to travel across country like you are planning. I would buy a good used, or inexpensive set of tires in the LT235/75-15 A/S size. Then later sell them for some better tires once you get established. But this is if your still running stock gears. If you had 4.88's, you would be good with 31's. But I would recommend upgrading to at least 8" wide wheels.
I have a stock 87 22RE with 31 BFG's on 8" wide wheels, and I can go to Bend in Central Oregon loaded and get an average of 20+ mpg easily. But with 31's, I find that in climbing Santiam Pass, I have to do 3rd gear and running 4500 rpm's just to keep moving. Because once you lose your rpms' and speed, your crawling, and hating the fact that your motor just doesn't have 20 more hp.
And later if you really still want to upgrade to skinny tires, I'd recommend going 16" and looking at the 265/75-16 variety in 6 ply. They are taller, and still are slightly skinny enough without going too wide. And Tillamook State Forest, (TSF) you will want some aggressive tread design. Like the Goodyear MT/R's or BFG M/T. Because there is enough slimy mud, that your are gonna need traction tires that can clear themselves easily. But there is ALOT of Motocross trails there too.
http://www.oregon.gov/odf/tillamookstateforest/pages/ohvtrails.aspx
