I see you are both redheads - so am I.
That means extra precautions - clothing and sunscreen.
Can you do the trip unsupported? Of course.
Should you consider the ST? Probably not.
The Western Express also has some long, remote stretches.
I'm guessing you have early June to late August.
12 weeks max. Biking and travel time.
60 miles per day - starting more slowly.
Plus one day off per week - for fun or to chill.
That adds up to about 4200 miles.
So you could do the traditional TransAm.
The advantages of the TransAm are excellent maps and meeting others.
I would suggest an east to west ride starting in early June.
Still using mostly Adventure Cycling routes -
You could do a Combo Northern Tier & TransAm -
Maybe cutting across Iowa and Nebraska to the Grand Tetons.
I think camping would be an important part of the fun.
But you should allow yourself funds for motels, as needed.
You meet a lot more people camping -
Plus the grandmas and grampas in RVs -
Will take good care of you.
Have fun! - - J