Suppose it turns out that the plan only requires that the dwarf get a large amount of iron in his stomach, and there is no affirmative need to actually chew the iron. He could then just break the iron chest into smaller pieces and swallow them without chewing them. No need to actually use his adamantine teeth, which are attached to his jaw with non-adamantine gums.
There is an actual guy who ate metal.
Michael Lotito.
Dude ate a bike once. He didn't just start chewing on the bike. He broke it down into its parts and swallowed the parts whole. He chased the parts down with mineral oil. And he didn't do it in a single sitting. It took a while. Exactly how long? I don't know. I've never eaten a bike.
(This guy died at age 57. So, he probably was not doing himself any favors by eating metal.)
So, if the plan falls apart unless the iron pieces have the character's teeth marks on them, then that will affect my ruling.
I need to know why. Particularly when players start spit-balling and improvising in real time at the game table.
I have answered this question to the very best of my ability. I don't know what else to say.