High Voltage 200V high frequency 1MHz pulse generator

The upper mosfet gate driver will not be sufficiently isolated if tied directly to a large battery.

It may be galvanically isolated, but the entire battery will be driven up and down with the load, and there will be a lot of parasitic inductance and capacitance associated with that.
Those periodic glitches look like some kind of fairly low frequency resonance or reflection.

The more conventional way to go about this, is to use a switching power supply, coupled to the gate circuit only by a very small pulse transformer to transfer floating gate drive power. That can then be arranged to have very low capacitance to ground for the whole isolated gate driver section.

The rise time requirement are not very demanding about 100-200 nano sec is acceptable.

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That could be produced by a high voltage sine wave, with just the top clipped off right at the load.
It would need only low side drive, either single ended or push pull.
A tuned tank circuit and the drive cable could then be made self resonant at 1mHz.
Much easier to get going with far fewer problems because there will be no really fast transient edges to cause trouble.

It appears something is triggering your hi side driver off multiple times during the desired ON time, this could be the UVLO on the hi side drive chip or RFI getting into it from a high dv/dt (or di/dt) source near by. Control ckts - including some gate drive ckts and IC's are easily affected by hi dv/dt (& di/dt) leads must be kept VERY short to reduce pick up (or use coax), de-coupling caps must be physically very close e.g 5mm, and low ESR, paralleled with an electrolytic (some ESR) to provide damping.
Check your drive signals are not the cause of the above (RFI getting in)
route hi dv/dt outputs away from control ete, use coax for o/p's or keep send and return wires together at least - don't make any loops...
Finally can you post your complete gate drive ckt as built - this will make diagnosis much easier...