What you want seems to be the hierarchy of Resources, that is, you probably want one class to derive from over (or being composed of some specific part and some common part).
Basically, ResourceBundle was not designed for it, and you are on your own.
But you want some advice, I suppose.
Make sure that common terms are really common. That is things like "OK", "Cancel", "Next >", "< Previous", "Open", "File", etc. will have common translations in their context. I mean it is fairly safe to translate such standard items only once, but if you want to use them in different context, you still need another entry. Why? Because "Open" button translation would be different than "Open" dialog title translation in quite a few languages.
Move all the .properties files to one place (for example a directory called "resources"). Of course module-specific files should be separated to different subdirectories...
- Create a resource factory that will return an instance of the ResourceBundle class (or your own Facade - this approach will actually let you share some common bundle).
The good practice for large applications is to create some Language Pack, that is to separate language resources to their own directories (i.e. /resources/en, /resources/fr, /resources/zh-Hans). The problem with this approach, however would be the fact that you would need to implement resource fallback by yourself (with the aid of an article you mention in the question, the hierarchy is actually resource loading hierarchy). That means some special cases like falling back from language tag "nb" to "no" but not falling back from "nn"; falling back from "zh-CN" and "zh-SG" to "zh-Hans" and then to "zh" but falling back from "zh-HK" and "zh-TW" and "zh-MO" to "zh-Hant" and then to your default language, not falling from "pt-BR" to "pt" (falling back to default language instead).
Seems like a lot of work? Well, but the maintenance work afterwards would be minimal.
One thing might come in handy PropertyResourceBundle have two constructors that will let you load whatever properties file you want, namely: PropertyResourceBundle(InputStream stream) and PropertyResourceBundle(Reader reader). Honestly, in large projects standard ResourceBundle mechanism has too many limitations, so you really need your own resource access layer...