You mean you don't like having migraines?

(sorry, couldn't resist)
Wow, it sounds like you have been on quite an assortment of meds. I am so sorry you have to go through this. I had almost daily headaches since age ten that got worse about 8 years ago. It took me a long time to control them (part of it was being diagnosed with HE and treated with steroids, but I don't think it sounds like you have HE).

Before the steroids for the HE, I searched high and low for ways to get rid of the pain.
As you probably already know, there's two types of treatment for migraines: prevention/prophylaxis taken every day, and abortive therapies like triptans or ergot derivatives on the days you get the headache.

They probably put you on the topamax to prevent the headaches. It's an anticonvulsant. Sounds like it's not working all that great.

There's 4 basic classes of medicines used to prevent migraines (prophylactics):
1. anticonvulsants (antiseizure medications which are also used in bipolar disorder too)
2. calcium channel blockers
3. beta blockers
4. tricyclic antidepressants

I failed a beta blocker (propranolol) and a tricyclic (amitryptalline- Elavil)
I was too scared about weight loss to try the anticonvulsants, so my doctor suggested a calcium channel blocker last year. I was skeptical to try the verapamil, but it really seems to do the trick even though I'm only on 40 mg at night. My headaches went from daily to once a week and the weekly headaches are controlled with Imitrex, sudafed, and/or steroids.

But every person is different obviously, so my answer is not your answer, and it sounds like you have already failed triptans and your headaches are stubborn.

It sounds like it might be helpful to discuss with your neurologist trying another type of prophylactic. You may have better luck with something in one of the other three classes. Your doctor should know your complete health history and should be able to help you select another one, if that's what you want and if he/she thinks it's a good idea.

I went into my third prophylactic thinking: "oh, so they really think this is going to work, huh... well not with MY headaches" but it really did work! I was so bitter and cynical that anything would work, that I almost didn't start the verapamil.

I don't know if any of this is useful or not. I haven't heard about the rib removal, but it sounds painful!

I hope you find some relief soon!
Best Wishes!