My first concern would be to ride the Northern Tier in good weather -- summer. Starting from Vancouver, I'd be tempted to ride it first so that I have better control over the time of year. If I rode it last, my schedule could easily change by 3 months as you noted, possibly moving me out of the window that I wanted.
The Southern Tier is much more leniant schedule wise. I might try to avoid it during the dog days of summer, but othersie I'm not too concerned. Also, I can't think of any one season having significantly less rain than another. The wind on it, like the Northern Tier, generally comes out of the south, so direction is also not too important.
On the Pacific Coast, there is a pretty reliable strong wind from the north. If riding from the south, you may get lucky and catch the one week or two a year that the wind switches, but more likely than not you will be fighting a stiff headwind most of the way.
I don't recall any significant prevailing wind on Atlantic Coast, maybe someone else can correct me. The timing on the two coast routes I think is more determined by what time you want to hit the Northern Tier. New England in the fall is particularly nice, as is California in the spring.
Adding it all together, I'm torn between going counter-clockwise to avoid headwinds on the Pacific, and going clockwise to control the time I'm on the Northern Tier. My final choice? Haven't a clue.