Best rate of climb is -125 feet/min. Depending on altitude, air density, and weight. All you can do is control your inevitable return to the ground.
Best check ride ever. The most interesting and challenging one was in a Super Cub on floats. Most the damn ride is sailing on the water. .
If you can manage a sink rate of 125 fpm, you’re equalling that of a high performance sailplane. Depending on altitude at which the engine failure occurs, that should give you plenty of time to sort out where to land. I don’t know what the Aztec’s effective L/D ratio would be in that scenario, however, so I don’t know how far you can fly to reach a given airfield. I’m also sure your foot on the good engine side is going to be getting mighty tired, unless you can trim it out.
As a (unfortunately non-current) sailplane pilot, I’ve always thought we should emulate the Europeans and require that pilots seeking airplane ratings first receive their glider rating. It really ingraines good judgment when every landing is a forced landing and go arounds are not an option. Sailplane pilots also learn good control coordination habits and learn how to manage their aircraft’s energy, all invaluable skills in an engine out scenario.