The bullet did not pass through the pleural lining of the chest.
I believe that it would have if JBC was sitting sideways as your idea dictates. It appears to me (and I suspect most of us) that if the limo is essentially pointed and moving directly away from the sniper’s nest (it was), and JBC is sitting sideways relative to the long axis of the limo, then the bullet entering his back below his right armpit would tend to exit on his left side (not near his right nipple). This is why I (and I suspect most of us) say JBC was not in a position to have the wounds line up the way they did during the time your idea suggests.
It hit his fifth rib. Turn around in a chair twisting your shoulders around with your seat facing forward and you can see that your right armpit and right nipple are in an almost straight line to the rear if not the nipple a bit to the left of that line. The bullet does not go through the rib initially because it is an oblique strike and travels along it. But it puts force on the rib pushing it in before it plows through the thinner end of it.
You are avoiding the fact that JBC himself testified under oath that he turned to his right again after he was shot. Your idea has JBC being shot after he turned to his right for the last time. There is a conflict here that you are apparently trying to avoid. Here is a snip from “Passion For Truth” by Arlen Specter, page 72:
At one point while viewing the film, Connally and his wife argued over whether the governor had fallen into his wife’s lap or she had pulled him into her lap. Connally insisted that he had fallen. Mrs. Connally insisted that she had pulled him. “No, Nellie,” “No, John,” they shot back and forth, several times. Eventually Mrs. Connally had the film halted and took Connally and Carr out to the hall for a conference. When they returned shortly, Nellie Connally and the governor were in agreement - on Mrs. Connally’s version.
Of course, I didn’t know what they said outside. But considering I was trying to gather a witness’s own account of the shooting, the Connally summit was not comforting. Later that afternoon, when the governor testified, he said, “So I merely doubled up, and then turned to my right again and began to - just sat there, and Mrs. Connally pulled me over to her lap.” His wife’s words.
I am not trying to avoid a conflict. I am trying to determine whether he turned left before he was hit. We all know that Connally later said he thought he had started his left turn and was hit facing forward after he had turned. I am just pointing out that he was not that clear initially. The last thought he had could well have been "I will turn left to see JFK" but he always admitted that he was not sure how far in that turn he had gone before he was hit.
It is at least interesting that in 1966 JBC posed for Life Magazine (Life, 25Nov1966:p. 48A):
I will admit that Connally may not have been the best witness as to where he was facing when hit. He may have had other things going through his mind. Nellie maintained that he was turned right when he was hit. SBT proponents want to accept Connally's WC testimony that he was facing forward, but refuse to accept his distinct recollection of the time gap between the first shot that hit JFK and the one that he felt strike him.