Commercial airliners seem to be moving towards twin jets with incredibly powerful 100,000+ lb thrust engines becoming available for use. Would it be possible to design the APU to provide enough thrust to push an aircraft to a nearby runway in the event they both fail as a safety measure?
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.
Keep in mind that the APU is a turboshaft engine, not connected to a prop but a generator. Therefore, any exhaust exiting the APU will have lost most of its thrust to the shaft turbines, or to bleed air used to power any aircraft systems that would normally be powered by main engine bleed air.
Sure, you could enlarge the APU to the point where it could supply thrust, but... it would be very inefficient as an APU (gas turbines don't run at low power settings very efficiently), it would add substantially to both weight and drag when it wasn't in use, and it would be essentially another main engine.
The whole point of an APU is to supply power and bleed air efficiently to an aircraft when the main engines aren't running... when it's parked on the ground. Typically, on an airliner, the APU also supplies bleed air to start the main engines if ground based bleed air isn't available. And typically the APU is small so it can be started by the aircraft's battery.
The keyword being efficient... for which it must be as small and light as possible, and consume as little fuel as possible. Given the very high reliability in today's gas turbines, an APU that can also supply sufficient thrust to keep the aircraft flying wouldn't be necessary, and would make for a fuel hungry aircraft.
Quote from Jane's Aero Engines 2017-2018:
APU: auxiliary power unit. An easily started gas turbine, usually forming a self-contained package inside the aircraft, which, either on the ground or following main-engine failure, can suply some of the following: shaft power, hydraulic power, electrical power, high-pressure aire, and (in a few recent cases, mounted in the tail) emergency propulsive thrust.