brook.reams
B Reams
I have to wonder if you are looking in the wrong place. I find it hard to believe that the brake shoes and drum could be bad, or be bad enough to give you pretty much no breaking. Have you looked over the linkage well and made certain it is in good condition and properly installed? I wonder if something is wrong with the linkage, binding, or perhaps installed wrong giving you a wrong ratio, wrong action?
Along the lines of the linkeage being the source of your problem, be aware you can install the cam that attaches to the external brake arm backwards. When you do, the cam does not expand the shoes fully and you get limited braking. This fits your observation of only part of the shoes showing wear because the cam didn't open them all the may, so only the leading edge of the shoes touched the drum.
I suspect when you replaced the shoes with new EBC shoes, you rotated the cam 180 deg and now have it installed correctly. So, now you have a rear brake.
The brake cam is (23) in this diagram.
The cam surface is not symmetric so rotating it 180 deg changes how much it lifts the shoes.
Hope that helps.
Best.
Brook Reams.