Another good approach might be to do it the other way around: Get rid of the pseudo-file-manager dialogs entirely and let applications integrate with the regular file manager.
I think RISC OS (?) did this. Open documents in applications had icons representing them which you could drag to the file manager to save. (And perhaps to other applications to open?) Mac OS also has (or had?) this to some extent – many document-based applications show an icon in the title bar, which is for dragging and dropping the document in question.
Even Windows has an example of catering to this way of working, in Explorer, where the folder icon in the location bar represents the current folder and can be dragged and dropped. They even have some custom behavior to prevent the window from being raised when you drag from it, so that it works more like classic Mac OS and lets you drag to an overlapping window.
Windows Explorer can be extended; the example I remember is browsing a folder of email message files, both the metadata attributes displayed in list view, and a functional content pane for viewing the message itself.
Be OS did this, too; I got the impression that Windows was inspired by that, both for BeFS (NTFS) and the desktop filesystem UX.
I think RISC OS (?) did this. Open documents in applications had icons representing them which you could drag to the file manager to save. (And perhaps to other applications to open?) Mac OS also has (or had?) this to some extent – many document-based applications show an icon in the title bar, which is for dragging and dropping the document in question.
Even Windows has an example of catering to this way of working, in Explorer, where the folder icon in the location bar represents the current folder and can be dragged and dropped. They even have some custom behavior to prevent the window from being raised when you drag from it, so that it works more like classic Mac OS and lets you drag to an overlapping window.