Shaun Inman created this cool rss reader (I've never used it, but every review I've found says it's really good, and the screen shots look really cool) called fever. It is a full text reader, however I think you can set it up to just show titles, and it organizes the articles by how much exposure they're getting, so you get the top news up top and the less important news (according to the twitter and a few other sites) lower down.
You could also setup your own system using the Google feed api. It's rather simple, and only shows headlines, but you'd have to create your own page for it and learn the feed api (which is pretty simple, but still, it's something you'd have to learn). If you choose this one you can contact me and I'll help you out if I can.
The last option I've got is to use Tiny-Tiny RSS, which is a self-hosted piece of software which you can infintely customize to suite your own needs (because it's open source), however you'd probably have to get into the code to fix it up exactly as you need it, but again, it could be done, and exactly to your standards.
