My impression is that my period symptoms are maybe in the top half of severity, but not the top quartile?
Don’t compare yourself to others. It’s a very common problem that apparently women especially have. You have symptoms that are distressing to you and are more than you want to experience AND THAT IS ENOUGH.
FWIW, I would definitely say based on your description you would be in the most severe 5-10% given when I am bitching about periods with friends who menstruate none of them talk about being out of action for 4 hours a month.
I think as well as what others have said, an ethical consideration with placebos is that they are treating someone with something that they know doesn’t work. Like, basically, on some level, it’s ethically dubious to make you go to all the effort you outlined, interact with medical staff, receive an actual injection, etc, and deliberately not treat you. That’s why many many trials have “stopping rules”, where if it turns out the treatment is working really well, the placebo group gets it, too.