They were going down a hill. The inclination begins early.
Lady Bird never said the car had straightened up.
So what is inconsistent about her statement and Jacks'? Only the driver is likely to be aware of when the car straightened out after making the turn.
Not far from being straightened out by, say, Z160 (allow a few frames for witnesses to perceive and process the noise) since the car is 70-degrees off Houston with just the rear trunk remaining to go on Elm. The driver said he was looking at the President, not gauging how straight his car was. He might later have had the impression that he had literally straightened up, but it wasn't the most important thing to remember.
There is no way to shoehorn Jack's statement with a first shot anywhere close to z160. Here is what the VP car was doing at z160:
Ready's head barely moves after Z199. So that's probably not where he "immediately" turned to his right.
We can't see Ready after z207. Before z199 he is facing forward to Zapruder's right. Between z198 and z207 he releases the left hand from the handhold and turns continuously to his right. By z207 his right hand is down by his right side and he is facing to Zapruder's left. He turns around to look rearward after z207 as we see him in Altgens' no. 6. taken at z256.
Between z160 and z199 Ready turns to his left and is looking left by z171. He appears to move his head right and left again just to look at the crowd in front on both sides - never behind or even to the side. He never lets go of the handhold with his right hand.