Add an "Edit as table" button on pages with Tabular.JsonConfig content, which opens a dialog for editing the data in a table widget. On clicking "Apply", the raw JSON in the editing textbox is updated.
This works similarly to the TemplateData editor for template documentation, accessible via the "Manage template data" button. Example: http://localhost/mediawiki/core/index.php?title=Template:Global_Heat_Maps_by_Year/doc&action=edit
The TableWidget editor is already in use for editing <graph> nodes via visual editor. Example: https://en.wikipedia.org/w/index.php?title=MATLAB&veaction=edit§ion=9 (click on the graph and go to the "data" tab)
Screenshot: