There's people around that could pretty much do that as one continuous ride, so it's hard to say what YOU should do. I'm with the wusses in Touring, and if I was doing it, I might manage 120 miles a day, but I sure wouldn't enjoy it, either. And, if I was doing it, I'd leave the tarp and sleeping bag at home and use motels, but that's just me. Most of the people riding long distance don't pack that much (intentionally) and most of the people packing camping stuff don't go that far in a day. You might load up your bike like that and go ride a few hours and see what kind of time you make with that load. That could be informative. Especially if you hit a nice headwind. (Going 350 miles in one direction, you COULD have a headwind the whole way. Whee!)
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"be careful this rando stuff is addictive and dan's the 'pusher'."