EinTerraner....
You're kind of breaking my brain here. I don't understand the question in the context of the example. Your example clearly already has a "sub-classed, base class", and in one tab you are showing all properties, in another you are showing favorite. You can make any property a favorite, save that class, and they will still be there. There are custom methods you've added (they are always at the bottom of any tab they apply to, and are always all lower-case and in alpha order, like those in your first example).
I would suggest two things:
1) Start a new thread, with a clearly stated problem, and what you are trying to achieve
2) Your "Question about Pageframe/Page" as Chris points out has nothing to do with these properties windows, nor the object "edit_container". So back to point #1, make sure it's clear what you are trying to achieve. I appreciate that knowing the answer you are seeking and the way you are constructing the question may not be related.
To that point #2, I think much of the confusion is, you know what you want to ask, but the way you are constructing the question, and what it asks is incongruent with the examples you are providing. SO knowing what you are trying to achieve is far more important than the question you are asking, because it seems to be in contradiction with the examples you provide.
We are all willing to help you get there, but please construct it in single, specific thread, and more about what you want to happen/behavior of the system or application, and less about "how do I do <something>", in a convoluted context.
Please don't take this as a criticism. It's not intended to be.