I feel your pain. I too got a Big Game Hunter 2012 for Christmas and was initially very, very frustrated. I have a 42" flat screen TV and had a lot of the same problems.
Here's what worked for me:
Sensor Bar - the one that comes with the Wii isn't very good, so I went to GameStop and got a wireless "Power A" brand sensor bar for about $20.00 (you can also get it online for about $10, but I needed to get it before nursing school starts up again). It has "extended range" which is apparently good for larger rooms and larger TVs. Yes, it "eats" batteries, but that's why they make rechargeables,which I'm using.
Sensor Bar placement - Mine's on top of the TV. It's really jerky if it's below.
Wii Sensitivity - I think I changed mine from "3" to "1"
Game Calibration - this also stinks and I think it's pretty useless, so I just turned it OFF on the game under "Controls" (press the "C" or "Z" buttons on the nunchuk to get to the right menu)
Dead Zones - I left mine at the defaults (60 and 20)
Top Shot Elite Gun - I removed the stock (button on the left side of the gun helps with that) and I removed the scope, since you really don't need it.
By the way, I have to stand about 6 feet away from my TV (you might have to get closer or farther). I've also found that Gallery mode is a lot more fun, since you're sort of shooting from the hip and looking at the cross hairs on screen, not trying to sight down the barrel. And there's more action in Gallery mode.
Maybe if the calibration actually worked it would add more to the game, but I'll never know. I saw in another post somewhere that Activision is aware of the issues with larger screen TVs, but no one knows if they're going to fix it.
Hope this helps.