I cannot give a difinitive answer having no experiance with the encore. The Contender is accurate for sure. I don't know if the break-open style of TC's is good enough for BR. I have a couple friends that BR & they have nothing but Bolt guns.
A possibility is a hand built heavy barrel in .22 with a match chamber & crown.
But I've never seen or heard of a BR gun like that.
I would call T.C. & see what they say if a bolt is out of the question.
Those are my thoughts; maybe someone has tried this & will give us benefit of their knowledge. GBO has a lot of readers & posters.