Hi, Ben. First, I believe that in the Cold Mountain scene in the church, the event is singing rather than preaching. The UK shape note site has an interesting review here:
Cold Mountain
The singers sit in this arrangement, divided into 4 parts - treble, alto, bass, and tenor. Dr. Warren Steel gives a brief explanation here:
Why do the singers sit in a "hollow square"? If you google "hollow square" and "sacred harp", I'm sure you will find much more.
But this arrangement, or at least similar, is used by some Baptist churches in the southern United States. I'm not sure of the history of its use, but am sure it has a history behind the current practice. I have seen this in several churches in northern Alabama and northern Georgia. The arrangement is usually only one row or maybe two behind the preacher, which is occupied by other preachers. Then there will be a few rows to the right and left of the preacher. Then the majority of the pews are out in front of the preacher.
The church where I grew up, in East Texas, had what I suppose were the remnants of this feature. There was a bench behind the pulpit, but no one other than the preacher ever sat in it. The preacher and a visiting preacher might both sit in it before preaching started, but would move to the side or front at preaching time. Then there were two benches on either side of the pulpit. A deacon or two, maybe a preacher once in awhile, used to sit there. And then there were lots of benches in front of the pulpit.
The pews to the right or left of the pulpit were once generally known as the amen corner. Also in early days, men and women were "segregated", one group sitting on one side of the building and the others on the other side.
I found this on the Lebanon BC, Roswell, GA site: "Most elements of the old services remain the same, but some, such as seating, have changed over time. Up until the 1930s, men and women sat on opposite sides of the building. Several benches to the left of the pulpit were the 'Amen' corner for the deacons and older men. The 'Singers' sat in front of the pulpit; later this was moved to the right of the pulpit, opposite the 'Amen corner' and they were called the 'Choir.'" I think you'd enjoy reading the entire page:
Lebanon BC History
Here's one in Texas that mentions the side pews: "The pews were home built and unpainted, as was the church building. I never thought of the pews as being uncomfortable. The faithful men sat on the side to the speaker's right. They were the ones who said 'Amen', when the preacher spoke. It became known as the 'Amen Corner.' Older ladies sat on the side to the speaker's left and all others sat out front."
Lydia MBC History
Also, First BC, Commerce, GA: "Inside there was a pulpit in the rear with a rostrum in front covered with red carpet donated by Mrs. C.W. Hood. In front of the rostrum was an aisle. On the left was the ladies' stove because the ladies sat on that side. On the right was the men's stove. The men were forbidden by custom to cross over to the ladies' side. On the right from the pulpit was the 'Amen Corner' where the elderly brethren sat. If a young man was particularly interested in a young lady, he made it a point to get near the partition. There were two outside front doors--one for the ladies to come in and one for the men. Married men usually brought their wives to 'their door' and then went to the other to come in on the men's side."
First BC, Commerce, History
It seems that the side for the men/amen corner may not have been consistent from church to church, or the folks are describing right & left from a different vantage point. First BC in Roanoke appears to have had benches only on one side of the pulpit: "The house of worship was a small unpainted building with a single aisle. Men and boys sat on one side; women and girls, on the other. Deacons and singers occupied the Amen corner to the right of the pulpit. There were no musical instruments and candles furnished lighting when required."
First BC, Roanoke, History
This may be a lot more information than you want; but some of this stuff I found is quite interesting (at least to me).