We are getting either the
2.50% of the tiles are available or
7.49 of the tiles are available
We do not have Clip Options in the Data Frame and we were zoomed out to the extent of the island/county when we created the Map Tile Package so those bases are covered. I tried using the "Manage Map Server Cache Tiles" tool in ArcCatalog today and got a 001390 error code: Failure to generate the complete cache.
As you can see in the screenshot it also says that the "workspace is not connected". Not entirely sure what that could mean since it still appears that we are logged in to our ArcGIS Online account. At this point we have to submit a Support Request to ESRI. I will post the results here when we have a resolution.