The to connect to MongoDB an additional layer is needed to help Tableau connect to the NoSQL db. The portion that you are configuring is actually something that was built by MongoDB and not tested by Tableau. I would reach out to MongoDB to ask the best method for configuring multiple servers for the Tableau connection.
Hope this helps!
You can try running separate instances of the mongosqld service and make them available via separate URI's. Then see if you can create a data source in Tableau across each of the instances using a cross-database join. That should give you access to all of your MongoDB instances in a single Tableau data source. Disclaimer: I have not tried running multiple services myself but I was considering this approach at one time and on-paper it seems like it should work.
Just FYI, In general, I have found that the MongoDB BI connector works well with cross-database joins to both Postgres and Redshift instances.