Forget about trying to discuss different medications, types of drugs, investigations, scans, or anything along those lines on this thread. None of it will help the situation because all of that ignores the underlying issue - the refusal to accept help, or even that there is a problem.
It might sound nonsensical, how can someone having such severe headaches that puts them out of action for 6-9 days a month not realise or accept that there's a problem, but people, especially men, are spectacularly good at willfully ignoring the obvious +/- convincing themselves that it'll be fine next time.
I've seen this from both sides of the coin, as a doctor and as a patient, specifically as someone with severe migraines. Now I'm on a load of prophylaxis as well as regular Botox, plus sumatriptan injections, nefopam and paracetamol when I have an acute episode. But by the time my now wife, then girlfriend, managed to convince me to see my GP about them, I was far worse than your partner, and I'm a doctor, I really should've known better!
It's not unusual to lose insight into how bad the pain is, and also, seeing your GP feels like admitting defeat; you've been beaten. However, it's actually the opposite, it's you refusing to be beaten, refusing to be limited and shackled and wanting to live and do the things you want to do without being restricted to a dark, quiet room for 3 days at a time.
That's how your partner needs to be thinking. Only when he does is the time to start talking about the drugs, medications etc.
Men can sometimes plain stupid, we find it difficult to talk to women, even our partners, about our health issues, our worries and ourselves. If your partner wishes to ask questions or talk to someone he can identify with, and who's been through the same painful journey, feel free to pm me and get in touch.
I hope things get better for him.