Thanks very much for your very helpful answers

I am planning on camping as much as possible. Snow is an unknown quantity to me - riding through it seems impossible to me! I'm very aware that there's safety factors there that I don't know anything about, and as I'll be travelling solo avoiding potentially dangerous snow conditions (possibly that someone who lives there would find routine) would probably be smart for me. Holing up in a hotel for a day/few days to wait out a snowstorm is definitely ok with me.
Cold and dry is good, cold and wet not so much but if it's for a day or two I think I'd manage ok. I live in the north at the moment so humidity is something I live with eight months a year and hate with a passion, so if I need to adjust my timing for hot-and-dry rather than hot-and-humid I'll do that if possible.
I'm aiming for later to give me more time to save for the airfare (and also time my time off work to suit my boss)! That being said, I'll be as flexible as I can to suit the weather and conditions so I enjoy my ride.
Time - I'm thinking about 11-12 weeks? Is that feasible? Slower than necessary? I'll be moderately fit by then but am by no means a speed racer, and I expect I'll be taking the mountain sections quite slowly but with longer days to make up for it in the flat stretches. I hope to catch the Coast Starlight train from say Portland to Los Angeles at the end, for the experience and also because flights home from LA are exponentially cheaper, but that doesn't need to come out of my cycling time ^