I personally really love the Fate system - it's much more hackable than other systems, so if a part doesn't work for you, you can usually tweak/remove it, and it sells "system toolkits" which essentially are homebrew guides.
Overall, I find most heavy systems tend to put a crazy amount of focus on combat, which skews stories into pigeon-holing combat whenever possible. Most players I run for tend to view combat as a last-resort, so it's hard to find heavy systems that match their playstyle.
Is there a reason you are putting limits on defining facts like this? Most games I play have flexible GMs, and I define facts (both beneficial and detrimental) on the fly for my characters. Of course, making sure things aren't broken/stupid are up to you as the GM - ie: a player couldn't declare themselves as a king (depending on setting/tone), for example, but a prince or exiled royalty would be more likely.
If you do want to use points and/or want to maintain a balance, I would recommend the story point system in SWFFG - where a player can spend a lightside point to define a beneficial fact, which turns into a darkside point the GM can use to define a detremental fact later. That way, players get their points back, and the story gets more interesting overall.