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James, the Inspector piece should be short-range but unblockable;
effectively a Guard-Squirrel combo, say. After all, they're not always
around, but when they show, they come out of the walls. (Literally [for
non-postal people], there are secret passageways for the inspectors built
into post office buildings.)
Larry, the WELOJDGWAAK piece could be a customer. You'd probably need a
special capturing turn, where multiple capturing pieces could all move at
once. Possibly the piece might need to be totally surrounded to be
captured. So cornering a 'Gwaak would be a good idea, making it easy to
capture.
It should be a large variant; I suggest the Registry Clerk (the Keeper of
the Keys) as a power piece;  some more minor pieces like the On-Break
window clerk and the Route Inspector; and finally, the 204B*, possibly the
most dangerous piece of all, subject to blowing at any time.
My condolences on your experiences with the USPS, by the way. I've been
retired 3 years now, and the nightmares are starting to go away. There is
hope. And, no, you can't blast the jam out of a machine by running more
mail into it. Believe me, it's been tried by experts. I've seen it, and 
it's not pretty. And then you have to put each bit of remains into its own
 little plastic 'body bag' which says on its side how the PO is trying to 
fix this problem. Right! You ever see anybody working on it?
* 204B: an acting supervisor; in other words, a clerk or carrier who
probably wasn't doing their job anyway, so it doesn't hurt to take them
off the workroom floor...