I think we have established that the MC is a DRUM / DRUM. The drum / drum MC has a residual check valve in both ports. If there is one in the port you have attached to the front discs you might be dragging the front brakes heating them up causing them to glaze or just plain overheat.
If you got a complete 68 system you will have the distribution / safety switch and a proportioning valve. No metering valve.
In the 67 thru 70 something KH system, the distribution block for disc or drum is the same. Down stream in the single line to the rear brakes is a separate proportioning valve. It takes the line pressure from (just numbers for example) 1000 psi and reduces it to 300 psi. That way the braking force for the front is in line with the rear. Otherwise the rear would lock up way before the fronts and you would be switching ends when you try to stop.
The adjustment of the rear shoes could explain this. Or shoes not broken in propperly, the backing plates could have worn spots where the shoes ride causing them to stick. Air in the system, Lots of reasons.