Don't know a bunch about the Audi servos/braking system, but here's my few views:
Remember that the servo is simply an assisting device, the push rod of the MC is still mechanically connected to the pedal mechanism, so in theory a hard pedal with the engine off should remain hard with the engine on. Obviously, you've disproven this.
It might be time to fall back to more extreme troubleshooting. I'd think about getting some 10mm bubble flare plugs and remove the brake lines to the wheel calipers one-at-a-time, replacing the lines with the plugs, and trying it with the engine running. If your pedal still plunges to the floor with all the ports plugged, you can bet it's a MC problem. If you get a hard pedal with just one (or more) of the ports plugged, at least you know where to start looking.
Why servo on/off makes a difference is a mystery, but it's just not possible that your depressing the pedal with the vacuum present can allow the push rod into the MC to not be pressed also.
You do have a Bentley service manual for this vehicle, yes? My A2 Bentley states that "vechiles equipped with the rear load-sensing regulator valve must have the load sensing arm held down towards the axle" while bleeding. Is it possible that the ride height of the car changes when the engine is running, making the regulator change the volume or pressure of the brake fluid going to the rear axle? Just freewheeling thoughts here...
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