My guess is that if you shoot a Henry Big Boy about 6 rounds a year it might hold up. I've been shooting CAS since 1997. I know shooters who tried the 'Big Boy'. I've never seen one complete a match without failing.
You might try going to a couple of local CAS shoots and seeing what's for sale. Sounds like what you need is an older Marlin Cowboy. BTW, I've killed numerous deer with a .357 Carbine. My Wife, my Daughter and My Son all took their first deer with a .357 Carbine. Stay within 100 yards and it'll do just fine.