I got a surprise: They called this morning at 11:45 and said my permit was ready. Naturally, I rushed right over, and now have a (somewhat oversized) laminated card that says:
STATE OF MINNESOTA
PERMIT TO CARRY A PISTOL
27 hours from filing to issuance. I'm quite pleasantly surprised. Despite the sheriff's publicly stated unease about the must-issue law, he did his job with alacrity and without the silliness other sheriffs have adopted (the sheriff of Washington County, on the southeast side of the Twin Cities, has taken to signing the permit cards and adding the Latin words "sub recuso", for "under protest"). I'll give the guy points for integrity, and hope that he'll come to see the people getting permits aren't the ones he needs to worry about.