It seems what you doing is probably difficult because it's not really a sensible thing to be attempting.
Multiple things come to mind...
* I'm guessing you're port forwarding public internet connections to your local private network in order to connect to the mpd stream, this is poor security practice.
* mpd's internal features/plugins is probably more suitable for the
mpd forum.
* If you get multiple site visitors connecting to mpd's flac-encoded http stream, this might quickly overwhelm your Pi and your internet connection's upstream bandwidth.
* nginx on your Pi is serving the Moode web application, it doesn't serve mpd's http stream.
* mpd's http plugin
doesn't seem to support https, hence you need to send to something like icecase or shoutcast.
* autoplaying embedded music & video on websites is generally frowned upon, modern browsers often block that by default.
Disregarding all that you could just provide a link to a hosted pls file that can launch the http stream in a client or browser tab.
Hope that helps though.