I'm not 100% sure, but I think I got it. I'm making this judgment based on the quick filter values I'm seeing in my dashboard after I made the changes. In short, I simply added the same field I'm filtering through the URL to the context and included all values. In other words, I dropped the pill in the Filters shelf, selected Use All radio option, and then selected Add to Context from the right-click menu on the pill. I need to see the actual query generated by Tableau, but I'm hoping that Tableau sees the URL parameter, identifies it as a context filter in the report, and applies the filter to the data source before other filters even though I've specified to include all values.