When at a Web page… click to send the URL to a script… the script parses the full-text page into a junk-cleaned Readability format… then passes that cleaned Web page into your personal RSS feed of articles.

This is now done by Tobias Franke, as a standalone .php script and a bookmarklet. There are a couple of caveats. You have to have paid-for hosted web-space, and space that won’t throw a fit over a new .php file. Also it relies on FiveFilters to do RSS extraction, so is not private. However, the maker shows how to use Composer to do the same locally.

See also: rsstodolist, but there your custom feed is publicly accessible to anyone who knows the address.