Sorry, I wasn't aware how complicated your case is! I didn't mean to speak like you were a drug seeker, I just wanted to steer you away from that route if you had other options still.
I don't know a lot about neck and upper spinal injuries. However, I think that a respectable headache specialist wouldn't give up so easily. There are many many different types of preventative medication. Even if you do have secondary headaches (caused by some other injury, that is), many people don't respond to the three prescripton strength medications that you've listed.
For example, I responded moderately well to zonegran, but not to topamax, even though they're both antiseizure meds. Then you also have bipolar type drugs like divalproex (aka valproic acid, depakote), lamictal, and lithium. Antidepressants and antiinflammatory medications can also be used as preventatives, beyond cymbalta and ibuprophen, naproxen. There are tricyclic antidepressants like neurontin and elavil; SSRIs like lexapro, zoloft, paxil, and prozac; SNRIs like effexor and cymbalta; MAOis (quite strong) like nardil, parnate, and emsam; and others like Wellbutrin, Zyban, and others. As for antiinflammatory medications, ibuprofen and naproxen are fairly weak and are rarely advised to take daily. Some strong ones that are sometimes taken daily are diclofenac, etodolac (lodine), ketorolac, indocin, and relafen. There are a few other strange ones like metergine, mexilitine (oral lidocaine) and various herbal remedies.
Also there are a variety of other triptans: Maxalt, Amerge, Zomig, Axert and Frova. I found that some work better than others. Many of them didn't work at all and a few helped a bunch more for me. And as for other abortives there are strong inflammatory ones like todadol, strong antipsychotics like zyprexa, haldo, droperidol. And things like DHE, lidocaine nasal spray, etc. You can try oral steroid tapers, since you said that worked. Plus Botox injections, nerve stimulators, etc.
Anyway, if you know all this, I'm sorry to make you waste your time reading. But I just wanted to get across the point that there are nearly innumerable types of medication and other treatments (and these are only the ones that I've tried); most likely you haven't tried many of them. Don't let any of your doctors give up on you.
RX: Lamictal, Abilify, Verapamil, Provigil, Clonazepam, Ambien CR, Rozerem, Emsam, Namenda