I was told the rule to install them was that it looked like the pad had slipped on the shoe with the wheel in forward rotation.  I Installed them that way in 2002 and my mechanic did it that way on a rebuild about 4 years ago. ( both times because of leaking wheel cylinders). My momentary locking up and loud clunk (on one side only) did not appear until recently. As stated, I pulled the shoes partially loose (without fully removing) and that gave me enough space to remove, examine, and reinsert the two brake adjuster wedges and screw. They were not stuck or worn. Since then the problem has mysteriously disappeared, for now.  Thanks, Harvey

I actually install the rear shoes facing in opposite directions. 

With both shoes leading as per the book, you have great brakes while going forwards but not so great going backwards.  Minis do very little rear braking when being driven but need effective handbrakes in both directions.  By turning one of the shoes you have one leading and one trailing shoe in both directions - my parents' driveway is quite steep and cars are parked facing uphill...

There might be a chance the brake shoes are installed the wrong way around. Typically brake shoes have a leading/trailing design where the friction material is shaped differently on each end or is not symmetrical, leaving more of the metal part of the shoe exposed on one end. Easy to get wrong. Also spring installation position is critical so they pull evenly and don't rub on the hub.

It sounds like it would cost quite a bit to have to replace them all Elastic man
  

Basically there are only two places grease should be in the rear brake drum, that would be the two angled pieces of metal that slide and move the shoes for the brake shoe adjustment. In the enclosed drum, the dust will just cake up on the grease. Back off the adjustment screw until you have enough grip for the parking or emergency brake. If it noise bothers you, take apart, clean and paint everything. If it still persists, replace all the components.