This time I fixed problems from log(7.5) about PWMed output of an Arduino, I added two voltage dividers as an temporary alternative, now they work as a reference voltage source:
And yes, it seems that everything works now!

First of all, about changing energy oscillation boundaries. There is three pictures, each is made with the same settings of energy oscillation, but with different voltages:

13V, as you can see, it's difficult for circuit to charge magnetic field as needed, so process of charge is really slow and uneven

15V, there you can see absolutely fine shape due charging process and adequate timings
18V, everything goes even faster, it's logical, because with greater voltage you can achieve target energy (current on coil) quicker

You can change oscillations of energy by changing reference voltages also

Well, what about conservation of energy now?
Here you can see current on a coil. I think it's legitimate to say, that there we see about 67% duty cycle

And also 15V VCC with 65mA power consumption.
Connected directly to a traditional driver with same voltage and duty cycle electromagnet would consume about 295mA, so we can talk about 78% energy retained.

Pretty good for 2.5$ worth of components! :D

Later, deeper investigation of circuit's behavior would be taken, as well - improvements, if needed.
As this schematics and theory was a source of 90% doubts and that's proven to be true and fully working - only a question of time to make remaining things. Even if not very fast - well, now it's 99.9% possible!