I don't think that is true at all.
Conducting or transferring heat to a "sink" can take a very long time. Heat is not "transferred" to work,
Conversion of heat into mechanical work is instantaneous.
I don't know how you derive that conclusion.if you're only bringing the fluid back to it's original size. That's why you would over expand it with a piston.
If you liken heat to elevation, expansion of a gas by adding heat is like rolling a ball up a hill. (In opposition to atmospheric pressure or gravity).
Let go of the ball, or stop adding heat and the ball rolls back down the hill, or the piston returns to TDC.
Also, when the ball gets back down to the bottom of the hill, does it stop rolling? No, you've stored up "potential energy" and an object in motion remains in motion.
In other words, by heating and expanding the gas, you set up conditions for an oscillation. The return back to contraction/cold tends to have a kind of momentum so that the contraction is stronger than the expansion. Like a ball rolled up a hill. When allowed to roll back down, when it gets back down to the bottom of the hill it tends to keep on going.
I think this is because on expansion you store. "potential energy" then on contraction "gravity" or atmospheric pressure is helping.
At any rate, this "hard" return can be seen in several videos and I've seen it in my own experiments.
"Over expansion" is not needed.But finding the efficient amount of over expansion will be tricky.
I think that may be putting the cart before the horseAnd I wonder if the engine in your video runs higher rpm because it doesn't have to lift up the displacer all the way.
Well, I think this is all certainly a departure from the "established" theories of how a heat engine is supposed to work, that has dominated for the past 200 years.After all that is sorted out in still not convinced it will actually be more powerful than a cooled engine.
My own tendency for extreme skepticism has kept me doing research and experiments for a decade rather than just building. I have not arrived at these conclusions easily or without opposition, and I have no desire to waste time, energy and money on something not based on experimental evidence.
Experimentally it can be observed that the piston returns to TDC "harder" than it went out with expansion, just like a ball rolls down hill much easier and faster than it can be pushed up a hill. I don't really need an iron clad theory to explain why that is, but it would help.