My pedals are forced forward when the back-pedal brake is on
What I'm guessing is happening is that your reaction arm (the thing on the left of the diagram) is not fixed in place.

When you brake the shoes of the brake are pushed out from the axle into the shell of the wheel hub. The idea being that the axle is fixed in place and the shoes drag against the shell.



If the reaction arm was undone, the friction of the brake shoes against the hub shell would be greater than the friction of the axle in the dropouts and so the whole unit of hub, axle and cog (fixed to axle) would turn under the rotational momentum of the wheel.

My guess is the 3 seconds followed by a noise is the time it takes for the reaction arm of your hub to overcome the friction and force its way past the chain stay.