You are missing all the points! So I am going to try one last time......................
Amps matter (Alot), if you want to learn then we need the figures. You are making wild guesses and assumptions and they are not accurate, what is going on is not what you think it is. I went through the whole thing myself when I started playing with electro motors etc, If you measure the Amps then we can show you how to make higher voltage and maybe make it more efficient.
The problem at the moment is my tests show that the first video couples with your motor, no doubt about it. If I hook a scope up to the output of the coil, and if I read the motor RPM, then what I see on the oscilloscope is a frequency that pretty much matches the motor. This was done without any magnet on the motor! Adding the round magnet made it slightly more efficient, but voltage was roughly the same. I am not sure how this side of things works, inductive coupling is complex. But if I had to make a few guesses then I would assume that the small magnet acts as a kind antenna (not the correct word), or it alters the resonate frequency.
If all you want to do is up the voltage then simply put a voltage doubler made with a couple of diodes and caps on the coil. the voltage will double and your light should still light. But you will have learnt JACK ****.
You may want to concentrate on the voltage, but I got some really bad news for you. This is lesson One if you like.................
In electronics/electrics is a family, this family does everything together. They will NOT operate separately!!!
One is the lanky tall weak one, we call him Voltage.
One is the smaller but beefier Brother, we call him Amps
And one is stubborn and resists most things, we call him resistance.
Now they only work as a trio, worse still they will only play with you if you use a set of rules called Ohms Law.
What I am saying is, you cant work with voltage and ignore the others. In your case the main one you also need is Amps, unless you measure this you wont know much. Your leds are not running at 7W (sorry), just cos it says 7W on the side dosnt make it so. They are leds and therefore a Current device not a voltage device like a bulb is. To light a led you need anything from 1 mA -750mA (high power ones). So you might be knocking out 200V, But you might only be putting out ~40mA. Double the voltage to 400V and your Amps would be 20mA.
These are extremely rough numbers, you are not getting 40mA
, but what I am saying is we cant help or teach unless you learn, part of learning is excepting that maybe what you think is true, isnt true.
I bet you used to think the Easter bunny was true, or Santa was true. Then you find out that only Santa is true. Well your kind of at that point at the moment. So go take the numbers, you measure Amps inline, that is the meter forms part of the circuit. I will google something for you later. Follow that and give us the numbers.
But seriously stop being stubborn if you want to learn, having played with this over the last few days, I can assure you that actually something way more interesting than a generator is going on. I can also show you a few cool things to do with your set up. But there is zero point without you measuring, all it would be is a party trick and a waste of time. If you learn to use the multi meter to take readings, then we can show you how this generator works, we can also show you how to fine tune it.
Last chance or your wasting my time.