iptables https transparent proxy with privoxy?
Solution 1:
A primary purpose of HTTPS is to prevent "man-in-the-middle", which is exactly what a transparent proxy like this is trying to do. To do so, you'd need to have a certificate valid for everything or a system to generate certificates on the fly. In either case you're going to need an internal CA (no already-trusted external one will give you a cert for anything you don't control) and to install that root as trusted in all systems behind the proxy.
Configuration of the browser proxy option will likely be a more reasonable task. It may be possible to do this through some sort of proxy auto-configuration, but I wouldn't be surprised if it's not possible for security reasons (I've never really investigated proxy autoconfig before).