A slightly spongy feel to the brake pedal can be the result of new pads. However, if that was the cause, the pads should bedded in enough by the time 500 miles have been done.
What is far more likely is despite the best efforts, there is still some air in the system. You only need a teeny amount to cause a feeling of sponginess.
For something that refuses to bleed, sidestepping the pedal in the bleeding process can shock the system into parting with the air.
I fixed a Landrover clutch pedal that way, and I know my father used the technique when a car was being obstinate.
