When I look at your page I’m not seeing the Mega Menu stack wrapped in a Visibility stack. But maybe I’m missing something. If you want to send me your current project file I will look at it tomorrow to see what might be wrong. When I create a new project file and place the Mega Menu stack inside a Foundry Visibility stack it works as expected, so I suspect the problem is something to do with your setup and not the stack, but I can’t know until I see it.
In fact now that I look at it, it should even work with Mega Menu in “sticky navigation” mode.