I did, however, go over to a new supermarket that just opened in the area and while I was there discovered that they have an in-store pharmacy. It's about one block further from my home than the Walgreens, so it's not at all inconvenient. A woman there (I'm not sure whether she was a tech or a pharmacist) answered my questions helpfully and gave me things like contact information and pharmacy hours.
Obviously, this could be a fluke, though they'd really have to work to piss me off more than Walgreens has, especially since most of the meds I take, I've been taking for a long, long time and with those meds I don't need much more than for them to put the correct number of the correct drug in a container. I have the information I need to transfer my prescriptions over to this other pharmacy, and that's what I intend to do.
The new supermarket carries Beggin' Strips, which the Walgreens doesn't, so my dog approves of this decision as well. He seems to regard me coming home with a bag of them as very very good service, although his opinion of me has clearly decreased since he discovered I don't plan to give them all to him right now.