super-glue and hex nut approach.
That type of back is a really good candidate for the rubber ball method, it does the least amount of damage when they're really stuck too
https://www.ebay.com/itm/123622036748
Crescent wrench perpendicular to the case back.
Don't know anything about this watch, but I hope you made sure it's actually a screwdown caseback and not just a snap-on caseback that's in the shape of something that looks like it would screw down.
If it is a consistent distance between sides, it should be easy enough to turn a socket for it out of aluminum. What is the distance between flats?
That type of back is a really good candidate for the rubber ball method, it does the least amount of damage when they're really stuck too
https://www.ebay.com/itm/123622036748