I've found a partial solution to my problem. I'm working with a 15,700-record dataset, and only 724 of the records have a GPS tag. This is the number I would expect to show in my maps.
So: rather that ask Qlik View to match the small GPS table to the large data table with a summary, I changed the GPS load file to include the summary field and re-loaded the data.
This seems to have done the trick; the mapping is quite spectacular and the required data can be seen, case by case, by hovering over a data point.