in hopes you'd get bored or tired and move on.

Fat chance of that! Nobody's going to get bored and move on from this story just because the bureaucrats stall on the files. That will just pique their interest.
I just don't see some bored civil servant counter clerk, whose vested interest is covering his ass with his supervisors, not serving the public, handing records like these over to you just because you tell him--or her--you have a right to see public records--which you do. I've dealt with people like that in a former job.
Sorry, I don't mean to be argumentative

, but I dealt with people like that all the time when I was a newspaper reporter. I wasn't a full-time cops reporter, but as a general-assignment reporter I often filled in at the police station or courthouse. The desk clerks are
very used to dealing with reporters. If they know you, they hand over the files when they see you coming, often making amiable small talk while doing so. Admittedly, many of the journalists in this case would be strangers. But whoever is on this story at, for example, the
New York Times (probably a handful of people, in that case) is likely a familiar face to them. Everybody involved, from the chief of police down to the counter clerks, knows the drill. I'm guessing that in this case they might even make copies of the report and hand them out en masse at press conferences just to reduce traffic in the office.
As some random member of the public, you'd have just as much right as a reporter does to see the records. But admittedly, it might be more of a hassle.