As you said it's not supported so I can't explicitly assist you with it, but I can tell you that v3 is based on nginx, and our initial tests started off with an unmodified copy of v2.2 running under nginx.
So it's definitely possible to use nginx instead of Apache without any modifications to Centova Cast, but you need to understand both Apache and nginx configuration well enough to configure nginx to emulate the .htaccess rules and so-on that we use for Apache. That's also why you're having problems with the widgets -- you need to set up appropriate location and/or rewrite rules in nginx so that URLs like /js.php/foo/bar are passed to /js.php.
You might even find it helpful to setup a trial copy of v3 and check out the nginx configuration it uses... the URIs are substantially different in v3, mind you, but it may give you some ideas.