I kinda hate to point this out, but in some states the use of non expanding bullets for hunting isn't legal. I expect this was intended to apply to rifles and military ball, but the legal beagles might not be that picky.
White tail deer really aren't that hard to kill if hit properly. Back when Remington was developing the .44 Magnum, they realized that performance on the WTD was key to the success of the caliber. The 240 gr SJHP was the result. I used this for quite awhile on PA WTD and never needed a second shot. Somewhere I've still got the one recovered from the first deer I ever shot with it. Entered the rib cage on a quartering shot and was recovered in the muscles of the opposing shoulder, just barely under the skin. IIRC it's almost 7/8 in in the largest dimension (oval expansion due to impact direction.). Come to think of it, all the deer I took with a handgun were with quartering shots.
The black bears I've personally seen taken weren't much bigger than a human. OK, they're fluffy, they might appear bigger. If you're in some area where you can expect the 400 lb + ones, a soft point or just maybe, a hard cast if you're expecting to have to break bones-and it's legal.