Why not leave as late as you can in April and do the entire TransAm east to west. Then if you'd like you can ride back down the pacific coast.
With your proposed route you'd be riding the least scenic part of the pacific coast, picking up the less than stellar scenery on the Southern Tier, and then missing the best part of the TransAm. Just my thoughts. Let's see what others have to say...
Especially since the OP apparently lives in the west, that is very good advice in my opinion.
You would probably have decent weather other than some rain in the east. You could arrange the long distance (air?) travel ahead of time. That works out easier because it is much easier to know the date you will start than the date you will finish. An open ended schedule is a big plus IMO. Set schedules (and budgets for that matter) can suck a lot of the joy out of a tour.
I also like starting out at the far end of a tour and riding toward home. That way you are automatically more committed from the start since you have no good options for bailing on the tour and by the time you are anywhere near home you are very road hardened and in the groove. Seeing family and friends again is a nice motivation to finish and if you are lucky friends and family can meet you at the end of the tour. We had family and friends meet us and throw a nice picnic at the finish of the TA. We were joined on the ride for the last half day or so by family members. It was a wonderful reunion.
Also, I agree on the relative merits of the various sections expressed by Miller.
I'd advise seriously considering the early start in the East.