Please do Pace.
Set yourself up on one, then reduce power so you are only holding altitude at Vyse. If you are light this will be a few knots below blue line (which is Vyse at MTOW), so experiment to find the speed which allows you to maintain height with minimum power.
Now, with that power set, do your bunt manoeuvre. You will have a height loss, a temporary increase in speed, but then, to maintain height, you will indeed bleed back to your min power speed again.
Next, set that same speed up and put in enough power for, say, a 200' per min climb. Now level off (no need to lose height) and accelerate to SE cruise. It will be a substantial increase in speed.
The error you are making is in your concept that the aircraft is somehow "Helped" by having more kinetic energy. The ONLY source of energy in a powered aircraft in level flight is it's engines.If it only produces enough power to hold level flight at minimum speed, that's the only energy you have. You can tap the potential energy of your height, but once it's gone, it's gone. Your increased kinetic energy is then robbed by the increase in drag because of the higher speed.
By the way, the Dragon Rapide would not maintain height in single engine cruise OR climb.