One problem with campgrounds, or motels for that matter, is that they don't occur at exactly the intervals you want. So if you need to average 100 miles a day, you'll have some 70 mile days and some 130 mile days, because that's just where you'll be able to find a place to sleep. If you're willing to sleep by any random spot by the side of the road, whether completely legal or not, you'll have more flexibility. Since you're under tight constraints, I'd try to plan out the whole route in advance including researching places to sleep along the way.
Some people tolerate heat better than cold, and others cold better than heat. You know which group you fit into. I rarely get overheated while riding because you have a constant self-made breeze. If you don't like the heat, you can start at first light, which also helps avoid the winds too. Anyway, the closer you can center your trip on June 21, the more daylight you'll have. Riding in warmer weather also allows you to take a lighter and smaller sleeping bag.
Remember that crossing the continental divide is a trivial part of the climbing you'll do. With the exception of the center of the country, there are hills pretty much everywhere. I wouldn't go out of my way too much to find an easy crossing of the continental divide--it's just not worth it to avoid a few hours of climbing. Many cyclists feel that there are a lot of places more difficult than the Rocky Mountains.
Also, if you go in the summer, you can ride Going To The Sun Road through Glacier National Park, probably the most spectacularly beautiful road I've ever ridden.