Great to hear. Thanks for following up.
Regarding access to the Mango database, remember that Derby is a standard SQL database that happens to be implemented in Java, so there's no magic to it. However, in this case, the properties of Derby that make it especially useful to Mango are the same as those that will cause you difficulty in accessing it the way that you want.
A bit of background; skip this paragraph if you want. Derby has the ability to run "in process" with a Java application, so that you don't need to, for example, start your database process, and then start Mango; you just start Mango and the single Java VM runs everything. This greatly simplifies installation and operation, as well as improving performance since the in process mode makes DB connections into lightweight objects, which also makes connection pooling unnecessary. There is also a small security benefit since Mango has exclusive access to the database.
The problem in your case is that Mango has exclusive access to the database. If you want to get directly into the Derby tables, you first need to stop Mango, and then start a Java process that itself would exclusively access Derby.
However, there is a way to get to the database through Mango, but it's not pretty. Recall that there is a SQL menu item in Mango from which you can run arbitrary queries and execute updates. It would be possible to automate a process of logging in, executing queries, scraping the results, and then logging out. (Told you it wasn't pretty.)
Better alternatives would be either to build into Mango the functionality that you want, or to build something like a web service with which more natural M2M access to the data is made available. Sadly, at the moment we are swamped and so will not be able to get to this for some time. Any enterprising Java developers are welcome to take a stab at it though. :)