The win_acl module just adds an ACE to the DACL of an object and doesn’t adjust the owner. Technically the win_owner module can do that but that’s only designed for files/directories and not registry keys.
As for your become_user: TrustedInstaller task, we currently can’t runas that user as it’s a bit more complicated than others. Unfortunately there isn’t an easy solution I have for you right now as they require a lot of manual PowerShell code. Maybe you can tell us why you need to adjust the permissions of this key?