I see that you are new here - and thank you for posting about your own experiences and concerns.
I have been serious cycling - commuting and touring - since my teens.
Since I am pushing 60, I can easily say I have 100,000 miles - at least 2/3s touring.
I have been hit by a car, sideswiped, has stuff thrown at me, and obscenities yelled.
It is part of who we are as a nation - and especially, to be viewed as "different".
To say that there are no risks would be absurd. But the risks are relatively small and outweighed by the benefits.
I was hit in my college years by a brand new driver - who wedged herself in a phone booth and was hysterical.
I went to the hospital for stitches and observation, but I think it took longer to get her out of the phone booth.
I have had stuff thrown at me - macho guys seem to like to toss soft drinks - ha-ha, so funny.
And I have been known to shout back at people yelling obscenities. (Which is not so smart)
There are ways to reduce the risk.
Fact is, it is more dangerous for a woman solo than a man - that is a reality of 2016 America.
My grad school roommate was in a relationship with a white guy and riding thru Tennessee -
Some rednecks slowed down beside and yelled, "Hey, n----- girl, your white boyfriend is way behind you."
And there are times in the week or holidays where it is best to quit early.
Depending on where you are riding - Fri & Sat late afternoon and evening may not be a good time.
And big drinking holidays - July 4th or Labor Day - can have lots of drunks on the road.
I may elicit some serious push-back on this one, but I have lots of touring miles all over the U.S. and Canada.
Not only are there more dogs in the South, I believe that the South is less tolerant of touring cyclists.
Outside of college towns, the South is more firmly wedded to the altar of the automobile.
Rail trails, wide shoulders, hiker/biker camping - tend to be found in the North and West Coast.
As is an attitude of tolerance towards people doing things - like bike touring - that some might never consider.
I know you mention the TransAm - which has lots of miles in Virginia, Kentucky, and Missouri.
(Southern Illinois and eastern Kansas have a pretty Southern feel, too.)
If you stay on the TransAm, there will be more cycling support - regardless of region.
And you will encounter other cyclists almost every day.
Other touring cyclists are rarer on other routes - rarer still if you craft your own route.
There is a trade-off, however.
On the TransAm you will be two of a parade that has been going on for 30 years.
If you chose to craft even a portion of your own route, you are likely to have a different experience.
It would be the latter case where region plays a greater role in overall comfort.
Obviously, I would not be posting here after 100,000 miles if I didn't think it was worth it.
In fact, I will be heading out on a 3000+ mile trip in two weeks.
Yes, there is some risk, but the rewards so outweigh any risks.
Physically, mentally, spiritually - you will never be the same.
US 6, Stone Cabin Valley, Nevada