Every engine failure at low altitude will be different.
Different in altitude, attitude, speed, there are no standard engine failures.
I stressed on the airpeed indicator, and would continue to stress on the airspeed indicator for a simple fact ; Every airplane behaves differently.
When loosing the engine in a climb, some airplanes will pich forward, some will pich upwards. God only knows at what speed or altitude you will be in when the engine quits.
Flying "by feel" requires a well trimmed airplane, with the ventilator running.
You add the extra task to retrim the airplane to be able to fly by "feeling".
At below 500 ft, there simply is very little time, and lots of things to do.
Also do not eliminate the "panic" factor.
The sudden and unexpected loss of engine, the time it takes to realise what's just happened. NO sound any more. SOUND is very important, and it's gone. The airplane is not talking to you any more as you expect it to do. Lots of "uneasy" things,. And do not forget the passengers either. They will start to panic as well.
Retrimming to fly by feel, will require the extra seconds and altitude you simply do not have.
Speed, flaps, speed, magneto's, speed, fuel cut-off, speed, and that's about it.
Speed is your life.
Sure you'll have more time in a J-3, and less in a Cessna or an Archer.
To add:
"Flying by feel."
Every flap adjustment, you would have to retrim.
Gear => Youd' have to retrim.
An unexpected engine out, is no time to fly by feeling.
Also, the engine is out.
No pressure blowing over the tail- or flap surfaces any more.
The yoke (or stick) will give you a completely different feeling as what you are used to, even in training, in simulated engine outs.