Have you looked at the OData feed? You can download submissions with Python, R, and more. Using Python, you should be able to download using pyODK and then push to your other database. You could set a script to run regularly using some sort of automation such as a cron job.
For an example, you can check out the code @mathieubossaert released to move data from Central to PostgreSQL. And he notes that "pyODK offers now the possibility to create pl/python function within your own PostgreSQL database or python autonomous routines":