I don't know for sure but if the "quick drive down a bumpy road" method doesn't free it off then getting the back wheel out, the drum mechanism out, and re-setting the handbrake adjuster is probably the only reliable way of sorting it out. There is a port in the back plate that is probably designed to allow the mechanism to be re-set with the tip of a screwdriver but on the M3W you'll need to take the wheel out to get access to the port so...
If you do take the wheel out I would suggest that replacing the locator block between the shoes with the adjustable type is a smart move, it really does make working on the brakes much easier.
From the Alternative Parts List it is; "Replacement manual shoe adjuster, mod to fixed item. AP Lockheed v4158-129 SP, Delphi LA18129, Ford 1560018, GM 9961958"
Have you heard any logical explanation of why the backing plate was not designed to i stall a few degrees off so the rear brake adjuster would be accessible while in the vehicle? It makes zero sense to adjust and pray you have it correct when you reinstall the unit.