I published a hosted feature service of code violations and, after a few days and lots of reading, managed to figure out how to get the time conversions between Mountain and UTC lined up so that the correct dates were displayed. My workflow has been to add new records to a local geodatabase (because that preserves the subtype-based default values), and then append them to the hosted feature service. Doing so automatically added 6 hours to the date, and there were no issues with the incorrect date displaying in the webmap popup.
Now, when I append, no hours are being added, meaning all dates are being entered as 12:00 AM, so that when the webmap subtracts 6 hours to display in my local time zone, it's the wrong date again.
Did something get changed to the way DateTime fields are handled when features are appended to a hosted feature service? This worked just fine up until recently. I tried updating ArcGIS Pro, but that didn't change anything.