Lets bring this back into context. We are talking about using Beta on short final, not reverse, or Beta at any other stage of flight.
Regarding an overspeed I’m still confused how one can develop in Beta. We are through the low pitch stops into Beta. The prop is disking. There is no positive angle of attack for the slipstream to drive the prop and we have a rapidly reducing airspeed. If there was any negative angle of attack the slip stream would be slowing the prop down. Why would the prop fail to come out of Beta? If there was a high risk of this occurring I’m sure certification with a Beta/reverse range would not have occurred.
I can understand an overspeed in a twin, when the live engine is maintaining airspeed and the governors fail on the other with the prop on the low pitch stops, but not on a single with reducing airspeed and the prop at a zero degree blade angle.
Regarding your last paragraph, there is no residual thrust. You land with slight Beta in flight idle, add a bit more Beta or reverse for free braking, when you’re settled and slow enough back to ground idle, push the power lever back through the gate, and roll up to the pad with minimal or no wheel braking. This does assume that the engine is correctly rigged of course. The prop is spinning faster but its not producing anymore thrust, it's in Beta, waiting to provide you with reasonably instantaneous forward or reverse thrust if you want it.