OK I'll bring this up again. The rear brakes should lock up 1st but not at light or normal conditions.

The O.P. said;
The brakes are all freshly adjusted by me and are just off the drums.

This will do exactly what is happening. The wheels will lock up right away because of the sudden contact.
Remember drums are a self-energizing system.

Just off the drum is wrong. There must be a slight contact.
Am I wrong or is this procedure wrong? Also new shoes on shinny old drums is not a good idea get 'em turned it doesn't cost that much.
What kind of master are you getting for $15.oo? Just a little curious about this.