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I can't answer your question directly but thought it would be useful to share some resources on custom admin views which may help:
The Postgress db that Tableau Server sits atop of containes all the data you will need with start and end-times of refreshes. It has been a while since I created any reporting from the server _ I can look into this when I reach home this evening, but the db uses a star-schema model and is fairly staright-forward to follow the complete data lineage.
I recall building a similar report for an alternate employer a couple of years ago, you would be surprised of the amount of data that is captured in there, the built-in charts are both not very useable especially when you have more than 2000 Tableau developers and 5000 workbooks, but they only scratch the surface of what you can achieve.