What happens with either drum when you put it on without the washers on there?
Is there a gap with the silver one, does the black one rub the backing plate?
Shoes: Measure the width of the shoe pad, measure the contact pattern inside the drum that was on the car when you got it, and the other too.
Can you explain a bit about the front discs?
Were the pads worn down to metal?
Did they replace the calipers? If so, are the bleeders on top or on the bottom?
Here is something to check on the discs if you want to take a minute. Jack up one front wheel, apply the brakes with some firm pressure and release. Now, try and turn the wheel, does it turn? Easy or with resistance?
Repeat other side.
If all they did was bleed them it's possible the rubber lines have collapsed on the inside and do not allow the fluid to return as quickly as it should, holding pressure on the pads.