electrolytic Caps often have a tolerance of something like -10% +50% for capacitance, as far as voltage a replecemnt MUST be equal or Higher voltage, and should not be MUCH more than double the original. So 360V IS equivalent. You may want to find one in the 220 to 400 Mfd range. at 360 to 400 volts (360v is a standrd value these days)
The values shown aren’t too hard to find, but the long and narrow form-factor seems to be used exclusively in photographic equipment. I know of no USA stock, and minimum orders of such parts tend to be large. But you might find a suitable replacement inside a single-use camera.
You could try, but I wouldn't pick such a high capacitance. The charge circuitry is engineered around that 360uF cap, which itself fits the flash bulb. Switching over to a higher capacitance may produce durability problems elsewhere in the unit. Just replace the cap with one of a similar rating.
If this will help, is uncertain, but such caps these days are cheap enough to give it a try.
One complicating factor may be that old electrolytical caps had much higher series resistance (ESR) than today's types. What I can't predict is how well the charge circuit will withstand the very low impedance of a modern electrolytic. It will probably work fine...