It looks like currently you can only set today's or a static date.
In this case, I do have one workaround that I'd like to suggest. Your team can explore the option of using the delay action before creating the Asana task. Here's a screenshot of how it looks like:
This way, the `due one` date would be set to the date that contact is scheduled for this task. The downside is that the task would be created 3 days after. I know it may not be the solution you're looking for but this can be one of the workaround your team can explore.
I can honestly see a use case for this request and if you haven't already, I'd recommend jumping over to the HubSpot Ideas Forum and posting this idea there so that it's visible to the HubSpot product team and other HubSpot customers and developers. Hopefully this will gather more interest.