We support time zones in the Azure Automation scheduler service. Azure Automation allows you to write code in PowerShell and execute it on a schedule. If you need time zone support now, I encourage you to check it out.
We’re currently making enhancements to the scheduler and investigating whether integrating local server timezones in scheduling makes sense.
Azure Update Management schedules are orchestrated and executed from the cloud, not the local machine. So time zones are required and using local time on the servers themselves is not possible.
Is there some reason that a Montly schedule with a 12 month interval doesn't work?