You have to have only one dimension as the axis.
Consider pivoting Start and End date. So you'll get two rows per [Date]. Column-A will contain either the value of "Start Date" or "End Date", and Column-B will have the full spectrum of date values. Call it [Project Date], for instance.
Then run your axis along [Project Date]. You'll need to account for duplication of measure values if you do this, of course. SUM([Cost]) will double count your values (unless you ETL this and place the values only in the "Start Date" rows or the "End Date" rows.
That's one way I can think of to get you there.
Thanks so much for the response!
I pivoted the start and end date, and so I'm now able to get the visualization to display start/end date. However, I'm having difficulty integrating the daily cost table into the view.
Here's how it's looking so far (see image below). As you expected, the data is duplicating, which is not a problem. But how do I get the cost data for [Date] to display as a bar for each day? In the final viz, I would like the daily cost data displayed by day.
I could tell you more if I had a packaged workbook to look at.
I would first make a sheet with [Project Date] as a dimension, and pump out text values first to see what things looked like.