Personally, I think the real issue is that the source of the evil happenings isn't the demons, it's the adamantine itself. Adamantine is the manifestation of pure evil in solid form, and only exists in places where the underworld and the world meet. It would also be reasonable to assume that hell is composed, in fact, entirely of adamantine.
It is not some kind of holy metal in which the gods sealed hell. If that even is the case, then how could you want the challenge to be ultimately surmountable? If the gods themselves resorted to sealing them off, as is the current norm for dealing for hfs, the demons are inevitable death.
You could physically defeat the demon hordes, year by year, season by season, but the true evil lies in the Adamantine. You may think this is not fair, as you could never give up this precious adamantine. The Adamantine wills you to think so. First it causes unparalleled greed and a drift towards malevolence. Then it causes madness, you hallucinate demons, have nightmares, and so on. Eventually you'll go berserk, or succumb to the will of evil entirely.
Your dwarves will become more and more influenced by the evil as they come into contact with the adamantine more often. All but the strongest willed good dwarves will find the temptation to steal beautiful objects crafted of it irresistible. Your thread extractor will likely be the first to succumb to the adamantine, sitting in a workshop for months on end processing the manifestation of pure evil. Also, ever wonder why your adamantine clad adventurer tends to slaughter entire towns of innocents without mercy? Increasingly weird things are bound to happen as the adamantine possesses the minds of the fortresses' denizens and fills them with evil. All of it should be as wildly evil and entertaining as possible, making for many self-writing stories.
There are few inevitable outcomes. You could avoid the temptation of adamantine altogether, casting any you come across into the abyss, or just not mining it at all. But we all know that dwarves are creatures of greed. Dwarves can avoid adamantine no more than adamantine can avoid toying with dwarves. Dwarves will ultimately either be killed by demons, or succumb to the will of the adamantine and become demons themselves.