How do I use a date created by a formula in the Timeline view?

I have a formula that checks a Due Date field start date, and if it is empty, uses a "rough date" instead:

IF (IS_NOT_NULL( [Due Date]),[Due Date].[Start Date],[Rough dates])

In a Grid View, this shows what I expect, and looks like a date. However this formula-produced date field is not available to use in the Timeline view.

I've tried wrapping it in DATE() and DATE_FORMAT() but these didn't work.

Any thoughts on how to make this work so that I can use formula-produced dates in the Timeline?