I finally had another look at this. I created a small demo project (pure Stage3D) and let that run on both Windows and macOS. It clearly duplicates the issue that pops up in Starling – it's working fine on macOS, but doesn't on Windows (edit: and surprisingly, neither does it work on iOS.)
So I created an issue for Harman to have a look at it.
Find it here: https://github.com/Gamua/Adobe-Runtime-Support/issues/392
So anyone interested in having this fixed right at the root, please vote! 😃