Other considerations in when to leave and what direction are your personal temperature choice. Do you HATE cold or hot weather? If cold, you may have to a start a little later. Of hot weather, you have to try to time it to avoid eastern Oregon and Kansas/Missouri during the hot parts of the year. Check the temps, winds, etc. over at WeatherSpark.com as they have wonderful climate data along the route.
Another consideration may be if you prefer to ride into the sun or have it at your back. I personally strongly dislike riding into the sun and am an early rider. Therefore, I tend to prefer E>W if wind is not an issue. If you are an early rider, when you ride eastbound, cars behind you may not see you as easily in early mornings due to being blinded by the sun. If you ride westbound, you may have less skin cancer (a major issue with me). However, the reverse is true if you depart camp late and ride until evening.
Other issue may be if you want to attend certain areas at certain times. If you really want to be in Jackson for the annual fireworks show (which seems to get cancelled due to fire danger more often than not), that may dictate your starting time.
Finally, how many overall miles per day you average factors in to several areas, i.e. temps, road closures, etc.
Tailwinds, John
EDIT: Changed words for clarity