I think an HDMI solution would work better in this case because you need as little latency as possible for music. The company I work for is considering trying a Blackmagic Intensity Shuttle or Intensity Extreme HDMI interface and converter, which cost US $300 at retail. I have no experience with them. You will need a Thunderbolt, PCI or USB 3 interface to your Mac to use a Blackmagic Intensity.
Part Two
I'm also a registered user of the Reflection app, and I've been in touch with their tech support staff. They point out that latency and frame rate depend on the specifications of the WiFi router through which the iPad sends its audio and video to the Mac. When you connect the iPad's video and audio to the Mac using AirPlay, are you using a WiFi G router (slow), or a WiFi N router (five times as fast as WiFi G)? Furthermore, you should probably connect the Mac directly to the router via an Ethernet cable, and not use WiFi on the Mac at all. Test this with a WiFi N (802.11n) router in close proximity to the iPad broadcasting with AirPlay and see if performance improves and latency decreases.
If you are using this setup in performance as a DJ, you might want to set up your own router in your DJ rig, whether it's connected to the Internet or not, so you can ensure the fastest connection between the iPad and the Mac.
If that doesn't produce acceptable results, then the HDMI hardware might be the next thing to try.
The Xscope mirror, a free tool works without needing VNC but you need a paid companion app on the Mac to send the data.
I prefer to use screens on the iPad. VNC is the way that OS X sends it's video remotely to another display. If you don't use it, someone else needs to re-write that entire stack and it works very well for local networks.
As for why the app I recommend, it has an observe mode and seems to scale the screen much better than the Xscope app since it is designed primarily for designing, not mirroring. The same program works on iPad, iPod, iPhone of all sizes and retina or not displays. It is very fast and has an observe only mode so that you don't accidentally send touch events.
If you do decide to use it on the go for remote access, there is a free location app (similar to how Back to My Mac works) and works over ssh tunnels if you prefer more security than speed. It has great soft keyboard support and of course works with Linux and Windows as well. There is nothing I can say bad about it in terms of missing features os bugs or design.
It's a quality piece of software all around.
If you really must avoid VNC, there is another option. The Xscope app for software designers has a free companion app that runs on the iPad and will mirror your screen. It's more designed for counting pixels and looking at mockups you design on the Mac for eventual use on the iPad, but you can use it as a mirroring solution. It lacks any input from the iPad and simply sends the screen from the Mac to iOS.
It also is very high quality software - and is well designed, all around and fast.
Best Answer
It seems to me that the frequency you have your laptop configured at is not supported by your TV.
When using mirror displays, it usually mirrors your main screen (resolution & frequency). Your main screen would be the one where you have the Dock and Menu bar.
Can I ask why would you want to mirror display on your TV? Is this for watching videos? If so, I would recommend you to do the following:
With VLC you can use your second screen on full screen mode without the need of mirroring.