Building anode voltage source from 5V

[Stan21]

I am trying to build a device to feed 6E2/EM87 indicator tube from 5V DC source.
I am going to ask a lot of stupid and straightforward question, would appreciate simple answers.
I am not going to use commercially available converters.
This project is 'return to the childhood'.

The restrictions for this project are:  NOT to use IC as a pulse generator and NOT to use commercial HV transformer. Actually, I am trying to reproduce a device I built when I was 40 years younger. The thing is I don't remember much about _how_ I built it, so I am guessing.
I remember it worked from 9V battery, and I definitely did not have access to ICs or HV transformers. There was voltage multiplier and probably 1 powerful Ge transistor, and there was a transformer on a large ferrite toroid core ('large' means ~3/4" outer dia). I guess pulse source was some kind of blocking oscillator (what else could it have been with 1 transistor?)

I want to build the one that has driving pulse generator, a transformer and voltage multiplier.
I need 200 V 0.07-0.08mA output, 4 stages multiplier.
So far I have :
555 timer at 5V/13 KHz as a generator, switching
D1616 transistor which has primary of audio transformer as a load
and 4 stages  cockroft-walton built with 8 15n/160v capacitors and 1N4007 diodes.
Primary of transformer has 14v peak-to-peak, secondary - 85V, multiplier output 370V DC - this is for idle mode
When tube is connected it drops to 190V which is quite enough for the tube to light on. Tube consumes ~0.07mA with cathode voltage 5V

Now I want stage by stage to improve.
1. Do I need diode protection for transistor load?
I put 1N4148 in parallel with transformer primary, the output dropped from 370 to 180V. So I figured inductive spikes are good for step-up transformer, but they are definitely bad for transistor. So should I ignore it or is there other simple way to protect the transistor?

2. Transistor is quite hot, so I want to replace it with MOSFET, like, IRF520. Again, do I need a protective diode?
3. I want to get rid of audio transformer and replace it with ferrite core. I don't want toroid and ordered a pot core 22/14
4. What can I do to minimize voltage drop under the load? I figured the transformer is the key here, is this correct? Like, the bigger is transformer, the less is voltage drop?
5. How do I make oscillator with a single power transistor?

I am totally not strong in theory. Why primary coil has 14V while the device is powered from5V? Voltage shape on primary is almost perfect rectangular, same as base voltage.