You're asking if there's something other than Evangelical American Christianity? There is!
I would like to recommend some podcasts to you!
The Holy Post: This is run by Phil Vischer (yeah, the VeggieTales guy), and Skye Jethani. They have some extremely relevant discussions about living a Christian life, without what you called "TRBC style"
You Have Permission: this is run by Dan Koch, a former musician in a Christian band (Sherwood), and he has some extremely relevant discussions concerning getting out of the evangelical mindset. I recommend ep. 123 especially.
For your reading, I would recommend: Skye Jethani's book, What if Jesus Was Serious?
Rejecting the tenets of Evangelicalism/Fundamentalism does not mean walking away from your faith, just that you're gaining a different perspective. Biblical inerrancy, strict creationism, the Bible as literature filled with symbolism and varying understandings of God throughout the many millennia it took to write it, the ultimate flaws of the apostles, are all tough things to contend with.
Finding a faith community that fits more into this mold, especially in the Lynchburg area, is challenging, though. Keep that in mind.