I did see the photo. The splines are worn. I had a '85 dodge pickup that wore the splines very similar to yours. It was a poor design with about 3/8 spline engagement. As it wore, I would notice the truck would dart left and right as I let of or got on the throttle. The more it wore, the more it would dart. I replaced the whole assembly and the funny darting around went away.
I have the '29-'49 parts book which states if you run the early axles marked 61 & 62, you can't mix the later axles marked 41 & 42. You need to run them as sets, one or the other.