Argh, I wish I had seen this in time for the bounty.
I do broadcasts using Camtwist. Camtwist will become a video source and it does things like just broadcast the desktop. So if you have EyeTV maximized and Camtwist broadcasting the desktop and your flash broadcasted using camtwist as a source, you should be set! If you want audio, soundflower is good for that, but not quite as straightforward as Camtwist. Might have to play with it. But there are lots of good tutorials on this online, give it a google.
To live stream your desktop, you will want to get two pieces of software:
Software to capture your desktop as a stream and redirect:
1) CamTwist - http://camtwiststudio.com/download/ - does desktop live capture and turns it into a video stream that is compatible for "webcam" input applications. I've used this to live stream my desktop to ustream.tv, Google Hangout, etc. (free)
AND
2) SoundFlower - https://code.google.com/p/soundflower/ - Allows you to redirect the system sound output so that it can be routed as an input for your stream (free)
Software to publish from your desktop:
1) EvoCam - http://www.evological.com/evocam.html - does a local http streaming server to serve your "webcam" stream out to the local area network. ( $30 )
OR
2) VLC - http://www.videolan.org/vlc/streaming.html - VideoLAN streaming component of VLC to livestream your "webcam" produced from your camtwist/soundflower combo. (free)
Can post more details, if this solution path works for you.
Edit: Note, a few test runs of VLC to export a stream crashes on my Mac. Looks like recent VLC builds support streaming the desktop, which is cool. With soundflower, you can also redirect the system output as well as the mic so that output from the apps and programs are livestreamed as well... provided your copy of VLC is running stably. :)
EDIT:
CamTwist is 32bit. So you will need to download the 32bit version of VLC for Mac OS X:
http://get.videolan.org/vlc/2.0.6/macosx/vlc-2.0.6-intel32.dmg
- Fire up CamTwist
- Select Desktop (not Desktop+) by double clicking it. This will add it to the list.
- Select "Save Setup", and give it a name.
- Go to [tools]->[Studio], which will pop up a new window showing a list of "sources", a preview pane, and a program pane. Your new stream probably shows up in "Program", which is the "live webcam" indicator. You can select another source via the buttons and it will show up in the "green preview" window. Hitting "cut" will cut over from preview to program.
- Fire up your 32bit VLC
- [file]->[open capture device]
- Under Capture Device, choose CamTwist.
- check the [streaming] radio box
- Choose the streaming settings
- Choose the [stream] radio button
- Leave most of the options as default
- Hit OK
- Hit Open
- This should start the stream.
On my box, my copy of VLC happens to crash at this point, but then again, my version of VLC (2.06 and 2.10) both seem to crash when I try to stream anything. So it might be a problem on my system.
But the above is how I get CamTwist setup and VLC to see CamTwist.
Best Answer
None of the devices currently connected to your television can help you display audio and sound from your Mac without hacking. And even then, it's not likely you'll get them to work as a wireless display/sound bridge.
You could use something like the Atlona PC to HDTV Wireless Adapter to send your audio and video from your Mac to your TV (that one is Mac-compatible). Are you going to enjoy this experience? I'll admit I'm very skeptical that this wireless streaming approach is going to produce a 1080p frame rate that makes you happy and comfortable playing a game. And at $200 that seems like an expensive experiment to me.
Your best bet is to get a HDMI adaptor for your specific Mac (see the Apple Store for compatible adaptors) and run the HDMI cable to your television. You can run HDMI about 50' before you need to start worrying about a repeater to ensure signal fidelity.