Cooper -
It is doable, but you offer little specific information.
San Fran - Denver - New York is one of the tougher options and directions.
Also, what season? Late spring/summer has the longest daylight for cycling.
And the heat shouldn't bother you, but the humidity may be brutal.
My favorite 3-month season is mid-May to mid-August.
It takes in late spring, but also has some dog days heat of late summer.
About that 90-day schedule with 30 for R&R - that leaves 60 x 50 = 3000.
Unless you plan on cycling the Interstates, it ain't 3000 miles on a bike.
I have worked on direct routes for years, and the best I can get is 3200 miles.
Adventure Cycling's TransAm is 4218; with SFO Western Express, 3750.
And do you want to go ocean wave to ocean wave or does Seattle to DC work?
I done almost a dozen crossings, but it's nice to do waves to waves on the first.
I really would not suggest a California start heading east - the Sierras are killer climbs.
If you must start in the West, I would choose Oregon/Washington - but you need to start later.
If you want to start in mid-May, I would start in the East and ride west.
I've done both directions, and the response above is correct - not much difference with wind.
Obviously there will be some bad windy days where you may want to chill out regardless of direction.
Crazyguy on a Bike has lots of good journals. (Gotta type in the address - crazyguyonabike.com)
Here's mine from 2016 - Washington state to NYC -
https://www.crazyguyonabike.com/doc/..._id=17976&v=UV
Hope you are able to do it. There's no reason you can't.
PS - I have the same weight yo-yo issue and I do it all the time.
PPS - I have found that there are better back road and bike trails the further north you go.
Most of the rapid growth in the past 50 years has taken place in the Sunbelt and road infrastructure hasn't kept up.
The northern states had a better road system earlier and this has persisted.
If you choose to make your own route, I would stay further north.