Android browser with reasonable private browsing mode?

Hi, I'm used to leaving my main browser open in private mode. It keeps tabs open across app/os restarts, but aggressively clears cookies in a bunch of circumstances. It also disables annoyances like autocompleting searches from browser history (since there isn't such a thing).

Is there something similar for Android? Vandium and Firefox nuke my private tabs on app exit, which isn't what I want. Basically, I want a web browser that is incapable of persisting state beyond the list of open tabs (and whatever crap they think they've persisted). However, since it is a daily driver, I want tabs to stay open until I close them.

Bonus points if each TLD gets a completely separate set of "persistent state".

Finally, I suspect I'm asking for too much, but buttons or gestures for "force reload" and "forward" would be amazing.

Has anyone managed to get something similar working?