Since the .page files generated by the system are rendered by an external rendering engine
I like to understand this structure change and more important, would like to know if it is possible to have the pages rendered in the old structure again.
Say what? You/they built something custom to render .page artifacts? If I read that right, you're so far off the supported path that you should have expected this kind of thing, especially jumping 6 years' worth of TS history.
LiveSite has page converters that automatically upgrade older page formats, but I don't know offhand if it converts your page whenever you edit+save it, or whether it does this at runtime.