Post the map on a separate website where it is large enough to read. When I tried opening it, the image was still to small to see.
Check out the website for Sylvia Halpern
Travels By Trike Home. She came through Las Vegas from Portland, Oregon last December on her way to the east coast. The route she took from Portland to St George should cover a part of you planned trip. She has made many of these trips around the US and in foreign countries. She probably has a pretty good idea of where to ride in all of the western states. She also knows how to plan an unsupported bike trek and probably could give a lot of pointers.
I's suggest your ride as much as you can between now and next March so that you are in good shape to go long distances and cope with some hilly terrain. If you live in the Las Vegas valley, there are some pretty good places to build endurance like the area south of the REI store in Henderson. If you don't do this, the first few days are going to be really rough. It will take months to build endurance so don't wait for winter to end.