Good question. With reference to the “Utilisation” setting within the basics tab of a Page, you can set it to be used either in an Interface or in a webpage.
The most natural way to reuse a defined page in both contexts, is to put the common content in a ‘sub-page’ (ie another page with a utilisation of ‘sub-page’), then use that subpage in both the wrapping Interface page and the wrapping webpage page.
I appreciate you then have 3 pages to manage instead of one, but by abstracting all the content into one place, you only need to maintain the content and workings of the page in one place. Plus you do then have a way to make some other parts of the page deliberately different.
To make it easier to switch to this arrangement, remember that widgets can be copied between pages.
To include a sub-page within its parent page, sub-pages can be included in a page’s cell, from the right hand panel (in the same way widget can be).
I did a very quick test with a simple form widget to check that this approach works but you’d need to test it works in your case.
Does that sound like a good solution?