Hi. You'll be fine with the 336 However, any rifle has far too much penetration. Even a .357. You are responsible for where any bullet you fire ends up. If the bullet kills somebody 3 miles away, you're guilty of manslaughter.
Mind you, skill, what you have and the bullet used matters too, but rifles have too much penetration. A .357 JHP is bit better. An AR is ludicrous altogether.
"...Tim is really into guns..." Tim while very likely a good guy, is a bit daft.
Where did your da's 20 guage get to?
"...stray bullets are a non issue..." Ever heard of a through and through?
"...only having two rounds on tap irks me..." If you need more, inside, a third won't help.