Can an APU be designed to also provide emergency thrust in the event of a double engine failure?
No, it would not be possible with current technology.

To scale the APU to an engine that provides thrust, you would basically have to turn it into another engine, with significant weight penalty. The position of the APU inlet and outlet would have to be re-designed, not to mention mechanisms that allow it to produce variable thrust. In short, it would be turning the plane into a tri-jet.

Furthermore, the chance of a double independent engine failure are slim. If a condition would lead to both engines fail, it would very likely lead to failure of any remaining engines. Converting the APU into a thrust producing device would be a complex engineering exercise with little to no benefit in risk reduction.

Perhaps decades later, we can produce a powerful jet engine using lightweight materials.