My go-to pain-relief used to be a product called Codis, which was soluble aspirin+codeine. It used to be available OTC, until about 8 years ago, then it disappeared. You can still buy paracetamol+codeine OTC ("Paracodol?). My understanding is that aspirin causes vasodilation, which causes more rapid absorption of codeine. Supposedly that's why Codis worked better than Paracodol.

I don't know why they took it off the shelves. There was no announcement; it just disappeared.

Codis was effective for both migraines and period pains, as reported to me (I'm not a woman, and I don't suffer from migraines).