I think it's going to be hard to do a hammerhead with the engine out
With enough speed you could. If I was 200 mph
at the surface in the Pitts and the engine quit, as
long as I pulled the prop knob all the way back to
get rid of the drag, I'm pretty sure I could gently
pull to the vertical and kick.
Like going supersonic with the throttle at idle. I'm
sure people here would say "impossible!". But back
in the early 60's my father's job was to transition
Sabre pilots to the -104, which of course had a reputation
as a fire-breathing dragon which you didn't want to
slow down.
What you don't want is a high alpha, which is not
quite the same thing. His favorite maneuver in the D
model was to show the Sabre pilot a hammerhead.
Pull vertical, throttle to idle. Wait for the airspeed to
get down to 40 knots - almost zero. Full rudder,
and watch the equivalent AOA indicator. Set the
vertical downline, leave the throttle at idle, and go
supersonic on the vertical downline, pull level.
What you can do is a function of your energy,
not the throttle. Different things. One day, he
was driving around the range at Cold Lake - primrose,
I think it was called. Boring as hell. The ground crew
in the building were bored at hell, too, and egged him
on for a full speed run. Ok, full afterburner, very low,
very fast. As fast as the -104 would go at low altitude.
Unfortunately the ground crew in the building stopped
answering on the radio. Anyways, it was throttle to
idle and coast up to 35,000 feet - with the throttle at
idle - and then just for grins, a practice forced approach
landing at Cold Lake, throttle still back.
Not many aircraft can coast up to 35,000 feet with
the throttle at idle.
Anyways, turned out things at the building at the end
of the primrose lake range were not good. Windows
blown, ceiling down. Quite a mess. Oops. Oh well,
at least they weren't bored, cleaning it up!
Edit -- a very, very long time ago, shortly after the
-104 was announced as Canada's new fighter, a USAF
pilot demonstrated one at Ottawa. Blew all the windows
out of the "new" tower!