Curiouse!
Only thing I can think of that would fit the symptoms described is if the shoes are binding;
ie;as long as the wheels aren't turning then pumping th epedal they do as they aughta. When you are moving though, movement between drum and show pulls the shoe into the drum (on the leading edge); then if you back off the brakes, piston is pulled back into the cylinder, but the shoe doesn't come with it, becouse the 'drag' from the drum is stronger than the return spring.
When you stop, load is taken off the shoe and it 'pops' back; if you were not to re-apply the brakes after slowing down a little, you might not notice; and it would pop when you next camne to a halt, or when it decided to.
But, I'm speculating; be interesting to pull a drum off and checkl whats going on in there; look for adjustment, both on clerance and alignment; look for weak or snapped shoe springs, or springs threaded through the wrong holes (They're a bugger to get on, and easy to put the spring in the wrong hole and get it on easier!) look for anything corroded or siezed in the mechanism, and estreme wear on the leading edge of leading shoe.
Put it back together and see if setting and adjusting sorts it out; if not, then I dont know, sorry.

well i had the same problem as you iwould suggest that you realign the shoes as they may be binding or if not try replacing the wheel single cylinders?

have you tried bleeding it???
u will get there!!