Hi Brett,
I was also looking for a way to automate the extracting of keyword data from Moz some time ago and hit the same wall. I have found a work around for it, which is far from ideal but does save quite some time. I have written an R script that uses Selenium to access Moz, authenticate and then get the URL that produces the .csv export. For example mine looks like this:
This makes the data available in my R session and then I can do pretty much everything I want with it. It is not an API so you won't be able to get the data straight into Tableau but you can save it somewhere and then just import the file. The script execution can be scheduled using Windows Task Scheduler if necessary. If you think this is something that may work for you, then I would be happy to share parts of the script.