To reduce the end play of the shaft, the impeller must be driven farther up the shaft. To do this, open the jaws of a well-anchored vise and place the pump in with the back of the impeller resting on top of the vise jaws. Tighten the vise just enough so that the jaws touch the nipple end of the shaft. This rests as much of the impeller backside surface area as possible on the vise. Now take a BFH and strike the castle nut end of the shaft several times. The end of the shaft is usually even with the castle nut, so no smashing harm will come to either. That's also why you are using a heavy hammer, requiring only a few forceful strikes instead of a lighter hammer and many strikes. In this case, fewer is better.
Anyway, as you strike the end of the water pump shaft, that will drive the shaft "down" and impeller "up" the shaft. After a few whacks, remove the pump from the vise and check for end play. You want the impeller to fit close to the rear bushing inside the water pump body, but not binding against it. That odd-shaped flat impeller spacer will help maintain the proper distance. If necessary, repeat this hammering process until the impeller is where it should be. You will note that it has moved by the change in color on the shaft where the impeller had been.
Once you have attained the proper spacing, TEST FIT the pump to the cylinder head. You have effectively moved the shaft deeper into the cylinder head recess, so you may have file or grind away some meat on the end of the shaft to make it fits properly and still be able to spin. The idea is to have the end of the shaft spin inside the special flat recess just inside the head. That was originally intended to supply initial "pre-load" of the shaft. As the years passed, however, that area is probably well worn down. You may have to taper the end of the shaft after grinding because as you go up the shaft past the initial factory bevel, it gets thicker. Test fit the pump without a gasket first. When it is correctly fitted, you may feel a slight resistance when spinning the shaft. Now try test fitting with a gasket in place. No resistance should be felt. Then you are done. You could stake the impeller in place with a small Allen head set screw, but generally this is not necessary.
Some guys may cringe at the suggestion of whacking the end of the water pump shaft with a BFH. But that impeller moves realtively easily. If someone who wears suspenders and a belt is worried about ruining the end of the shaft and/or castle nut, he can remove the nut and re-install it backwards until it is flush with the end of the shaft. Then bang away! I have made loose water pump shafts with too much end play serviceable again using this procedure on many Model A's. It works!
Marshall