The current training emphasis is that we should not mess about trying to make a dog's dinner into an unlikely successful outcome. Better to make full use of your height and time identifying a safe place to land and planning how to do so. An engine giving some power will help to maintain height or at least flatten the descent so extending the time available to plan and provide more options. Having identified the landing place then commit to that and carry out the plan.

The syllabus doesn't state at this point that the aircraft should be shut down but rather thorough and comprehensive checks are to be undertaken with the plan underway. So, if you discover that the: mags are switched off by knees, your passenger has pulled out the mixture control or the fuel selector is miss-aligned then obviously correct things. Having corrected these unambiguous faults and the engine now runs as normal then continue with your plan while still checking that things are indeed good before going on your way. If the recovery is temporary then you will still be in your plan to land. Should you be forced to land statistics are that the outcome will be good. The aircraft may be wrecked on landing but the pilot and passengers will likely survive.

Messing about without a plan in the hope that you will find an obvious fault but continuing to lose height or by leaving behind a good landing with the wind now against you surely doesn't make sense. The statistics for this idea are not good.