That is a beautiful pen to start you down the collecting rabbit hole. LOL
It almost sounds like you are mixing the two systems up. Forgive me if I'm mistaken.
Converters are designed to take liquid ink directly into them. Cartridges, like the ones you have, carry the ink instead of the converter.
If the converter in your Parker is still good, then all you need to do is get yourself a bottle of ink. Is your converter still working, if not it can be repaired.
You can also pickup a new model "Parker" converter. They are still proprietary, but are readily available.
Unfortunately the cartridges that you have are what is known as "standard international". While they fit many different pens, yours isn't one of them.
Parker cartridges are available in many stores, as well as online outlets. These are what you would look for.
I have also heard that Montegrappa long cartridges may fit, but I don't personally know.
The advantage of converters, is that you can get an infinite number of different colours, while cartridges are much more limited.
Reach out if you have any other questions.