Running several versions of a MySQL database in parallel?
One must separate: What do you want to "version"? The interface or the data?

Versioning the interface

If you only want to version the interface, you should (must) manage one single base of data and provide it in different formats at different interfaces. Otherwise you will run into consistency issues, if your data should change (and even geo data changes -- the rarity of changes makes it even more vulnerable to consistency issues, because this is done so infrequent that humans tend to do mistakes).

In this case I would use one single database and VIEWs for different interfaces. This is harder to setup, but saves headache in the long run.

An alternative would be to replicate the data periodically by a cronjob, which might be a waste of resources if this changes very infrequently.

You could also implement a script and make somehow sure it is always executed if some data changes. (Vulnerable to human errors this is.)

Versioning the data

If you want to version everything including the data, your approach seems fine to me. Although it might be more efficient to just use another database instead of a completely different server instance.