I tried everything until my hands hurt then read about melting shellac in a metal container and putting the case in, allowing the shellac to cool then turning the case body to unscrew the bezel. I realized after making a huge mess that I did not have the right pot so went with a variation on the theme.
I used the appropriate size Forstner bit and drilled just deep enough to keep the bezel seam above the plywood surface. Out came the hot glue gun and I gooped it in the depression. I got it wrong the first time, not enough glue, then on the second attempt masked off the seam just in case.
Here is how it looked after the glue set up and the masking tape was peeled off.

A latex glove for some purchase and a big grunt resulted in an awful crunching sound but it broke loose. I was afraid that crossed threads had made the sound but couldn't tell right away as I could only turn it a bit because the pendant was trapped by the plywood. I had to drill an escape track for the pendant and crown.

Off she came, crunching all the way. Turns out the sound was from the green gunk brass corrosion. This is not a high end case, Tornado brand with little if any of the original scant amount of gold left.

I poured in a bit of lacquer thinner to release the glue, you can see it progress by the colour change. A bit if very gentle prying and out came the bezel.

I was worried about breaking the crystal but it also came out unscathed.

There is the green gunk causing the problem.

This seems a bit of a harsh solution but it works to remove the gunk. I have used it on a better quality gold case to remove some red gunk and it did not affect the gold. It can take some time, hours to be honest, apply, clean threads with a brass brush and repeat, and repeat, and repeat.... You can notice it's affect on the colour of the brass, it is actually a radiator cleaning product and contains phosphoric acid, use nitrile gloves.

And there she be.

CLR or lame away works great no scrubbing just mix some in some water and let it soak for a few minutes.

I have found that doubled sided scotch tape works well for bezel or back. Just put a piece across either, just enough to cross the entire watch, then it should screw off easily.