So what does the PCB do ?? Do they make high voltage or maybe high current pulses to do some DPF on a big metal surface ??
What are the input supply voltages, the upper right cap is probably for input supply, and maybe the lower C9 also, I'd try and trace back to see if it's just a part or 2 away from some input voltage rail.
Is the top circuit with C4, a buck converter making a lower voltage for the big main MCU chip in the middle ? What is the label on the IC by the big square 47uH inductor, or is there none ? That looks like the only step down or step up converter, or there'd be some other big inductor.
What about U7, any label ? There's a lot of circuitry and then that big MCU, I wonder what sensors hook up to this also.
For C9, you could use some through-hole cap, mount it sideways, and glue it down. Depending on the PCB, I might drill some holes also, if I was going to use through-hole caps, and try and solder down a big long lead, to say, a big bottom ground plane.
If you don't care about brand new parts, and have an ESR meter, I bet you could find suitable through-hole caps, in some modern TV that someone's giving away or throwing out.