Let me know if this is already possible and I’ve missed it.
One way to implement this would be to allow the user to write “Fri@4pm” as the due date, and Asana would automatically implement this as a date and time.
Another way to implement this would be to include a keyboard shortcut for adding a due time.
I’d welcome other ideas for how to implement a due time using keyboard shortcuts.
I had the same need and decided to build it a few years ago and have been using it daily instead of Asana’s date dialog almost exclusively. It keeps my fingers on the keyboard and saves a lot of time.
This is accomplished with Asana2Go (Disclaimer: I’m the creator).