The odd thing was a connection timeout exception was never thrown. Perhaps I didn't wait long enough to see it though. I was able to get past this connectivity issue when one of the engineers reminded me about the proxy settings configurable in JDeveloper.
When I checked the command that JDeveloper was executing, it did have a number of proxy parameters specified, these were...
I wasn't setting these explicitly anywhere, but there was an option to enable proxies in the Project Properties. To access these, right click your project and select 'Project Properties...'. You will see a dialog box pop similar to the one below.
Click Run/Debug then select the Default configuration and click 'Edit...'.
On the screen that pops up, select 'Tool Settings' and untick 'Use Proxy'.
After I did this and ran my code again, it connected without any problems.