We had a thread on tranny testing a while back. ISTR the idea was to apply some DC, break the circuit and see if there was enough inductive kick back to light up a neon. This will find shorted turns.
To check ratios, apply a low AC voltage to a winding and measure across all the others. Take care when doing this because if you put 6V on a heater winding you'll get a nasty surprise if you touch the primary
Same goes for an output tranny putting volts on the speaker side.
The resistance imbalance on your output tranny is most likely due to one half of the winding being inside the other and so has a shorter length of wire. Not many are bifilar wound. I don't know what a realistic balance accuracy would be but I'd be surprised to find even a 5% error.