With the Arkenshoes revelation, I've had a flash of insight, and I'd like to put my new theory out there.
The Arkentools are not of this world (that is, not of Erfworld), and all have a particular relation to erf/stupidworld.
* The shoes can return people to stupidworld from erf
* The pliers can yank people from stupidworld from erf (and from the dead back to erf).
* The dish can be used to communicate with people from stupidworld.
* The hammer can ultimately be used to destroy erfworld.
Supporting arguments: We know that Judy probably came from stupidworld, and probably will return there. She had a special relationship with someone conjectured to be Charlie. Charlie might have been the one who invited her to Erfworld, via the dish. (How she actually got there is another question).
Wanda is so far the only one we know for certain who has broken the barrier and pulled someone from stupidworld. Granted, she wasn't attuned to the pliers at the time, but she was fated to. Yanking people into the world and binding them to service is kind of what she always does.
Charlie has knowledge of stupidworld, more than could be expected from a friendship with Judy, assuming she's from a 1920-version of stupidworld.
The hammer thing is, I admit, a bit of a wild guess for symmetry's sake.
But the important thing is what happens now. I predict that the Friendly Pyre has already made the fire impossible to control, guaranteed to escalate to inferno. Parson can't put it out, and he can't move out. He can't save anyone. So what does he do?
Tries Charlie's scroll. What's there to lose? If he tries to be noble about it, Jack may even use it on him against his will.
And actually, Charlie's scroll does work, and Parson is returned to stupidworld at the end of the book - temporarily. But Charlie/the dish/the pliers, maybe even the shies provide a way of getting back - and maybe even bring along some of his friends.