It really turned out, when I looked at the panels in the dashboard, that the queries that had been copied over when the dashboard was cloned were just all very confused. They were looking at the wrong template variables and using the wrong filters etc. My work was to clean up the queries, so they all work. I didn't know whether the group would prefer to make the filter a template variable and only display one filter per panel, or if displaying all filters in each panel would provide more information, so I made an example panel showing how to do each of those cases.
I think that does the spirit of what was asked for in this ticket.