TOPIC:

When I have the bike on the center stand and spin the rear wheel to adjust the brakes, I have to loosen the adjuster nut more than I would like to get the brake pads to not rub in one spot. Leaving  it adjusted there causes the brake peddle to depress farther than I like when braking. I do not feel any pulsating in the peddle. 
What things would cause the pads to rub for 60 deg. but not the other 300 deg. of rotation? Always rubbing at same spot.

You brake shoes are worn out, minimum brake pad thickness = less wheel drum brake diameter = less drag surface area.
Don´t safe money on brake shoes or pads!!!

How old are the brake shoes?  If you don't know their age, replace them.  The adhesive that binds the linings to the shoes can fail >> a lining will break loose then get jammed between the shoe & drum, locking the rear wheel. It happened to me, so it does happen. I was lucky the wheel locked in the driveway when rolling the motorcycle off the center stand. At speed would be a real drag.