"...its gates were wrought of mithril and steel"
Okay, we have a serious problem with mithril gates. Mithril is VERY rare, and extremely useful. I have wanted to make mithril gates before, but SERIOUSLY? EIGHT mithril ingots for 4 gates? Wow... that is a LOT a lot. My suggestion is very simple.
Instead of eight mithril surrounding the one gate gear, I suggest have it be four mithril and four iron, since in the books, the gates were wrought of mithril and STEEL. So, since we dont have steel yet, we can use iron. Yes? I would say four mithril ingots for four gates is a lot more fair. And besides, mithril was said in the books to be all lost or hoarded by the trolls and orcs long gone. Where did the dwarves get enough to make such a big gate basically PURELY OF MITHRIL? Makes no sense.
Also: Mithril would bend but not break, and stand firm against any attack once it cooled and made ino the actual armor/plates/whatever needed. I believe that mithril gates should be "special" in order to actually make them USEFUL, because it is true. Hobbit gates are just as useful and strong as mithril gates.
So, bombs and explosives will NOT damage mithril gates. Everything around it may break, but the mithril gate will NOT.
Second, it will take just as long to break mithril gates as it takes to break obsidean. (its mithril, lore-wisely, its supposed to be invincible, but... you see the problem with that.