There are a few things that can affect extract speed. One of them as you found is the number of joins in when performing the extract. One workaround would be to extract them individually and join the Tableau Extracts together.
Try reducing the size of the extract as well: Tableau Data Extracts - Tips, Tricks and Best Practices | Tableau Software
The speed of the two different versions of MySQL I cannot speak to. I would possibly post in the MySQL community asking more specifics about the differences between Community and Enterprise. If the Enterprise version is faster than in turn the connection/extract process could be faster.
Hope this helps!