What technique are you using to color your regions? You might be able to average the latitudes and longitudes of that set of zips to get your labels all stacked on top of each other near the center of the region. Then there's a IF FIRST()==0 formula that might work to trim that to a single label.
Yes putting these together on a dual axis should work just fine, especially if you don't want labels on both map layers. Rather than going the shape route, you might find it easier to just take a screen shot of your regions, add whatever labels you want (even nice legends, including a scale indicator) and then use that as a background map image. The first one will be a bit tricky to set up, but after that it will be easy to swap out your data sets.
If you can post a sample packaged workbook, or a data set, I can get you started.
Thank you for your email. I was able to make a very bad work around for the interim, but still need a better solution for hte long run. I am attaching the source data that indicates the "DISTRICTS". They are effectively stratified by zip codes.
I am a little nervous about the screen shot idea because each time I run a new map, it will insist upon always been the same sizing to use the layered photo. For my work sometimes I need to zoom in on an area and other times zoom out... depending.
But welcome any thoughts you may have on how to get this going.
Thank you for taking the time!
District Data for Tableau.xlsx 23.7 KB