Using JQuery to trigger the button will not work, as Cross-Origin policies would prevent the jQuery Trigger event from working.
I ran into this as well while attempting to make an Amazon FireTV WebApp for our own channel. We have “Mature Content Warning” enabled, and the Embed does not have support for the FireTV remote control, preventing any sort of control. In addition, the FireTV does not support Deep Links between apps (even WebApp to Native Apps) so we cannot simply redirect a WebApp user to the Twitch FireTV app and auto-load our channel.
I would hope that these types of features appear in the Embed, FireTV Twitch App and FireTV as a whole, but Im not holding my breath.
The only other NON-OPTION would be pulling video via the M3u8 playlists, but that is against Twitch ToS, and as stated, is not an option what so ever.