Well, bummer. Another GOTCHA.
After I opened a case regarding "Overwrite" not being available, "Overwrite hosted feature layers" documentation was updated yesterday to highlight that this capability only works if you publish the hosted feature layers by loading a file geodatabase or shapefile and choosing to create a feature layer at loading time. However, the doc does not note (today) that if you published the hosted feature layer from ArcMap, that Overwrite is not provided as an option. Today, that information may only be on this little post in the untraveled hinterlands of GeoNet.
Note that if you publish the hosted feature service from a file geodatabase so you can use Overwrite, then you lose metadata (e.g. description, copyright text, constraints, tags, display field, min/max scales, etc.) in the item and in the service catalog. Also note that layer names are not generated from feature class aliases if you publish from file geodatabases. And, I'm not seeing a way to specify max records returned. Kind of a miss.
Since retaining and presenting service metadata when publishing from a file geodatabase is not supported and other capabilities are missing, Overwrite is of little use to organizations who have a requirement to make the metadata available at the service endpoint along with their Open Data offerings.
I'll have to stick with Scott's customization above until the file geodatabase publishing tools respect the GDB and feature class metadata. Disappointing for our purposes.