If you have fitted standard diameter shoes but your drums have been ground oversize the shoes will only be contacting in the centre
When you pump the pedal the shoes are actually bending to make contact around the drum.. and when you apply the handbrake the same applies.. .the shoes are already in contact
So I'd say try there first

Or you have the calipers on the wrong sides of the car (if thats possible) and the bleeders aren't at the top
Air rises.. and can be trapped high if the bleeders are low