I can't create a hunter's license for Blue Burst, or for any other version of PSO for that matter. I've tried may times with many different browsers just in case that was an issue, with no luck whatsoever.

Not sure if this was resolved for you, but I'm experiencing the same thing I think.

I click on MyHL and a modal pops up, but there's nothing there except a language selector.

make sure your in https
you can try to go there directly: https://api.schtserv.com/MyHL/