I changed my home to Latest and I’m happy with that.
For the first suggestion, it seems like a mix of self-ordered & latest. As a user I’d probably be confused since I expect to see admin-ordered on the normal home page, and time-ordered on the Latest Posts page, but not a mix of the two on the latter. Would I like to have a 3rd page that works as you said? Perhaps. But on the Latest Posts Page I wouldn’t want to have the site “interfere” with my intent to simply see the latest posts.
For the 2nd item, maybe you can create a “meta” post that instructs users how to mute categories they don’t want to see? Of course having a feature would be easier.
(Btw, did you see this topic (and similar)?)