As you already know, the old stock bearings are probably pitted and worn. I have replaced them with a set of sealed NSK R8Z bearings. I also have a new 1/2" axle.
The bearings measure 1 1/8"x 3/8" with a 1/2 hole. I used a roughly a 1 1/4" diameter shim that was 1/16th" thick. There is also a spacer between the bearings. These numbers are approx. and may differ a couple thousandths.
I am in the process of doing this for my front Worksman brake drum as well.
I think I have like 20-25 bucks into the rear.