I think an engine failure at 450' in a PA28 won't give you time to think much to be honest. It almost has to be instinctive at that height in that type of aeroplane. Nose down, pick a point and aim for it, end of! ... You'll have no time to worry about shutting down, cracking doors as all your brain capacity would (should) be channelled towards just flying.
Also, in my experience, engine failures are rarely so obvious or immediate which can also confuddle the brain! A slower loss of power leaves you wondering what's happening which is actually far more dangerous than a "bang, splutter, stop" situation.
SS