I don't use an Encore but I do use a Contender. My brother and his son use Encore muzzleloaders and they each have a rifle barrel as well (.280Rem and .260Rem). I use my single shots for rabbits, grouse, pheasant, raccoon, deer, elk and coyote. I use it in .22RF, .410, .30-30, .45-70 and .223. Used a TCR87 in .30-06 for moose and a 10ga barrel for ducks and pheasant (loaded down).
I got into the Contender carbine for its light weight, reduced length and multiple barrels. It's small, it's handy and I've shot it enough since the early 1980s that reloading is more natural that cycling a bolt action, even though I grew up using a bolt gun. It's the little brother to the Encore, but I like it better. I did think the original Contender stock is slightly better looking than the new one or any of the Encore stocks.
If I need more power than what I get from my Contender, I think I'll buy a Ruger #1 /ubbthreads/images/graemlins/smile.gif
Sometimes the Contender and Encore are very accurate from the factory and sometimes they're not. Many of those who struggle with accuracy in either platform do so by treating it as a bolt action. They're a different animal, if you treat them right they work!
If you like the Encore/Contender concept then you'll have fun with it. Many people will do better with a bolt gun, and there's nothing wrong with that. NONYA makes some good points in favor of a bolt action - there are circumstances where one is better than a single-shot.
Choosing any single shot over a bolt gun is no different than choosing archery, muzzleloading, handgunning or opting for an AR. They all work, choose what you like and adapt your hunting style to match.
Oh, I'm not from the east. Born and raised in Washington state, living in Utah.