Refreshing brakes - what should I look at?

So Dad's car (69 340 Swinger) has drums on all 4 corners. He doesnt plan on racing the car, but he does plan on driving it. As such, I dont think we need to swap to disk or anything trick, but rather make sure the current brakes are in working order. I pulled the drums for the front and checked them out. Everything inside looks good (almost new). I think I will probably just pop the whole assembly off, tape off openings, clean the backing plate, paint, and be done with it... unless you guys know of a weakness (other than being drum brakes) that I should specifically address? Either front or back.
Brake clean, drum back on, adjust shoes till the drum, when back on, spins about one turn and stops.
Use only brake drum paint if you do that, dont bother with the backing plate..they will be dirty in a matter of days.