I've found with a lot of modern shoes that the heels are too long or badly shaped - where the heel of the shoe sits in the wheel cylinder and the brake adjusters is subtly the wrong shape.
If you offer the shoes up to the drum they are probaby the correct diameter and round enough to work. When they are sat on the hub they can effectively become an oval by being pressed out too far.
*If* you can wind the adjusters in far enough to get the drum on (not guaranteed) the the contact patch is tiny.
2 minutes with a file to dress them back to a more acceptable shape and you'll be fine.
First time I did this after working out the problem was a revelation. Went from failing on brake efficiency to a handbrake-turn monster in half an hour. Not had rear brakes so good since the late 90s...
My hand brake is really inefficient at the minute despite adjustment, I wonder if this is the issue. Can you stick on a picture to show where you file material off?
Thanks.