I use timer 1 for one note and timer 2 for the other note. For now the signal has no noise.
 If you want I can post my code 

Thanks for the answers.
I added off time to the code and I don't think the sound quality is much distorted so maybe I'll try it on DRSSC .

Hello,
I wrote the code for arduino based polyphonic MIDI interrupter, for my DRSSTC, that can play 2 notes. But I don’t know if the pulses can overlap or be close to each other (like the pulses in the picture)?
Is it safe to run the coil with this pulses?

Since my chip (UCC27423) didn't arrive in time I couldn't wait any longer and just inverted the UCC27424 inputs with 74HC14 and also adjust a phase lead a little bit , and now DRSSTC works perfectly.
Thanks again for all your help.
Here is some videos.

Can I just invert the input signals (2 and 4 pins of ucc27424) with 74hc14?

Here is some scope images with and without a screwdriver and circuit of my driver (Vge - blue trace). 1kHz 200us on time - input signal. I connected only GDT ,without OCD and feedback CT .
A similar thing with a screwdriver happened before IGBTs exploded. I wrote this in one of my past posts.

I`m scoping primary current with another separate CT (41 turns connected to 41Ohm resistor).
I've already adjusted phase lead before with proper oscilloscope as best as I can, so now I`m afraid to adjust it again (unfortunately I had limited access to that oscilloscope). First picture that I posted is taken by that oscilloscope.
After some experimenting at low voltages I decide to power bridge at full voltage (310VDC) and the coil didn't work at all (only some small sparks at 7KHz and 9us on time).
Then I replaced switching power supply which powers the driver (24VDC 10A ),because that's the only thing I didn't check, with classic iron core transformer with greatz , some capacitors and 24V regulator and finally the coil works (still skipping some pulses at low frequencies below 100Hz but it does not matter) 
I guess there was some interference between driver and switching power supply 
The coil produce around 30cm sparks at 200Apk , 1.5KHz and 30us on time. Given that the secondary is only 23cm tall I think this is a good result.
I'll post a video soon.
Thanks for all your help, especially davekni for the great tips and explanations.

Vbus is 24VDC.
Yes , the third picture is of the current feedback (450:1 on 51 ohm load) and yes , anomaly where the current reverses is repeatable. I think that's what happens when the gate signal have small duty cycle ( second picture).
I didn't know that for double emitter terminals. I'll fix it as soon as I can.
I'm using four paralleled primary wires but i patched them to a single pair of wires right next to the GDT.I shielded all wires with aluminium foil and put everything in shrinking tube.
In my local shop I can only find these caps for MMC so I hope that they ( 68nF 8kV) can handle  4.5 kV peak at 150kHz. I checked all the capacitors separately , with RLC meter , and they are all good.

After my last post  when everything was worked , yesterday when I turned it on again nothing worked as it should. So I just don't know what to do 
That's happening from beginning , one day it works and when I try the other day it doesn't work properly. Only works if I connect signal gen.Than I reduced feedback CT turn ratio to 1:450 but results were the same.
In attached img can be seen gate signal ( yellow trace )with CT  connected to the feedback input. ( blue trace - current) It's weird that things get a little better when I touch one of the feedback inputs with a screwdriver 
What can cause this behaviour , driver , CT , GDT or something else?

I only use signal gen as feedback input because when I connect feedback CT nothing works( also with reversed wires ). I used 4 turns on my previous core with high AL value (11400 nH/turn²). I'm using power supply with adjustable voltage (14v to 24 v) , so I adjust voltage to somewhere around 17 v to keep Vge overshoots under 30v and I use the same power supply for Vbus. ( 1.5KE27CA TVS is connected across gate emitter). I connect 10Mohm res across every capacitor( 4 strings of 4 in series).