This is what I had in mind. I tryed to follow the code to undertand how the admin page edit page works, with the idea of replicating it in a minimalistic form, as you decribed, but I get lost in the complexity of wp.
I couldn't find the function that retreives the page contents to the edit form, nor the funtion to save the changes.
Other problem is how to call the same page with two different page templates, one for general use and the other for editing. There are some plugins for switching templates or themes for especial users, but this is another level of complexity.
A brute force approach could be to use a second wp installation working on the same database, but I don't like the idea very much.
At this time, I can get the page contents, as it is stored in the database, without any wp filtering, inside a textare. Now I need to save the changes, but I don't know how to doti, and better, how to bypass the user identification of wp. I need this operation extremely simple. A link sent to the user should make it all, without login, usernames or passwords.