How did your 58 come to have a "Lockheed" axle in it anyway? The changeover to the later axle was in 56, at the same time they introduced front disc brakes.
Not sure what you'll find, since it was apparently previously converted to the early axle; but as noted the threads at the soft line from the axle to the rest of the car are different between the two axles. But maybe you'll get lucky, and the Girling line is already there.
The 9" brakes provide a little less braking than the earlier 10" did, but probably not enough to matter unless you are going racing. Supposedly the factory made the change because people were complaining about the rear brakes locking early, but it's never seemed like a problem to me. If you find that you do need more bias to the rear, it's relatively easy to install larger rear cylinders in the 9" brakes.
Turn each flange with your fingers for several revolutions, to feel for any roughness. This one just had a little rough spot ...
If it feels good and the oil looks good, I might be tempted to skip pulling the cover.