Brightness is much more easily set. Bring up a gray ramp (0-100%) and adjust it so that the bottom ~10% is identically and completely black.
Contrary to what its name may lead you to believe, "brightness" doesn't actually adjust how bright the screen is. It actually adjusts the so-called "black level", which is the signal level at which there's insufficient drive to the tube to make it do anything i.e. it's totally black. This can be set "correctly".
Contrast is a bit more fudgey. Basically, set it so that it's "bright enough for your taste" without blooming. Causing doming like you seem to be experiencing is pretty extreme. I'd expect it to be exhibiting other artifacts first. Given how often people seem to experience this problem on these monitors, I have to wonder if they have crummy shadow masks in their tubes that easily deform or absorb lots of energy and heat up unusually fast. Regardless, set brightness "correctly", then just keep turning down contrast until it doesn't do this.