I did a little more testing. If I open up a previously-used document (from several weeks ago), and try the copy-paste, the style works as it should, and the text comes in Minion. If I open up the new template I made yesterday, however, I first get an error that Times (TT) is missing. I thought, AHA — there's where I can set the document's default to Minion, right? So I changed that. But when I tried the paste it did it AGAIN. It is determined to use Times!
I wonder if I should actually create the template in CS4, and then open it in CS5, and see if it works any better. Off to check ...
Check the type spects in Basic Paragraph as well as in the Character panel with nothing selected, and make sure that [None] is selected in the Character Styles panel..
I even set [Basic Paragraph] to match the incoming style I wanted — and had the Character Style set to [none] — and Times overrode it again. It's determined, if nothing else!
I may have solved the most pressing issue, however. I opened up a month-old newspaper file and repurposed that into a template. The copy-paste thing worked. It doesn't explain the cause of the problem, but at least it's a work-around. I'll just keep 20- and 24-page versions available depending on which size I'll need.
It's still a head-scratcher though.