Welcome to the forum.
Unfortunately, I don't think I can help very much. Tthis is really a dermatology more than STD question. Dr. Hook's and my experience with genital warts is pretty much limited to initial diagnosis and treatment, and we (and most STD clinics in the US) refer patients with problems like yours to dermatologists.
My general advice is to first assure that the recurrent lesions in fact are warts -- but of course if your cryotherapy is being administered by a dermatologist, presumably this hs been done in the course of routine care.
All wart treatments do exactly what the cryotherapy is doing: they treat the wart tissue, not the HPV in surrounding skin. However, when warts continue to recur with any particular treatment, it is often worth trying an alternate method. Other options you could discuss with your derm include laser cautery,podofilox, imiquimod, and others. (In theory, imiquimod's immunologic mechanism of action might be preferable to the others, but I stress "in theory". In fact, it's probably no more effective than other methods.)
As for the alternative therapies you mention, there is absolutely no scientific evidence that vitamins, zinc, etc have any effect (and really no theoretical biological reationale why they should). And although Gardasil is being tried experimentally against established warts, it has no proved effect against them and I doubt it will make any difference.
Sorry I can't suggest a magic bullet. But eventually your warts will stop recurring. In the meantime, I hope these comments will help guide your discussions with your dermatologist.
Best regards-- HHH, MD