Have you tried combining the instructions on adding background images to a map with the instructions here: Plotting Two Sets of Latitude and Longitude on a Map | Tableau Software
I'm not positive it will work - this is indeed a tricky task - but could be worth a try.
Hope it helps!
Thank you! I tried this earlier, but the limitation here is that for some reason Tableau has a thing against treating generated latitude/longitude values as the same as uploaded lat/long values, so I can't just treat it as if I have two separate conventional lat/long datasets.