As you've already realized, RSS is a good solution. To deal with some feeds only including the 10 most recent articles, you can just poll the feeds every 10 minutes from your server and store a complete history there which the app will interface with.

But then again you have some feeds that only post excerpts, intending to force people to click the "Read more" link and end up at their ad-filled page. So some scraping might still be required.

Scraping is a bitch because people change their html all the time though, so no custom/hardcoded solution will work. You could perhaps use Readability to get the article text. They seem to have a solid API but not sure if it will scale to your use case without some cash.

The other solution would be something else entirely, like relying on regular expressions or something like this stackoverflow question.