I have never crossed the entire country, but I have been on tours that took 8 days/nights to reach our destination. Sleeping along the way is no dif on MY tours than on your X-country tour. We had the same problem, but we rarely got turned down when asking a someone if we could use a small patch of grass to set up our tent for the night. It did happen, though, from time to time, but its nothing personal. The land owner just does not know you or your intentions. If you are clean, look like you have EQUIPMENT (not junk) on your bike, and perhaps have on a cycling jersey and helmet, most people see you as "harmless". You just have to get over that "first time" of asking a stranger for a small patch of grass to set up your tent. If THAT fails you, you may have to resort to some stealth camping. We would wait till no cars were coming, then quickly tuck into a brushy area to the side of the highway. If a passing motorist saw us tucking into a brushy area, they just thought we needed to pee and never give us a second thought, let alone report us. As long as you dont jump over any fences you should be ok. Dont be afraid. This may soon become your regular routine and its not bad at all. I wish you the best and hope you get a good nights sleep tonight!