Seamonkey. With a bookmarklet to go to the archive version of the current page (to bypass paywalls), it can do everything you want. If, as suggested by your want of self-hosting, you want something centrally located that will allow you to seamlessly track feeds across devices, all options suck, whether paid or free. You're probably better off just writing a program in your language of choice (I've never seen a language without one or more RSS/atom-specific libs, let alone plain XML) to meet your own needs rather than banging your head against the wall of someone else's pet that does what they need but isn't perfect for you.