I still don't see why the engine should be running when bleeding the brakes.
What kind of information would the ECU need?
The car is standing still and the brakes are not used!
Or do you bleed the brakes without using a tool?

If the brakes would work relatively ok I wouldn't spend $450 and would wait a few months to see if they improve.
Maybe the air will be slowly absorbed by the brake fluid.
Would make an emergency stop and have the ABS kick in to see if that goes fine.