Sounds like the bullet you used worked just fine. But, honestly you're overthinking this. Any jacketed lead bullet 160 gr and up designed for hunting will accomplish your goals. Bear rarely go straight down when hit, but it doesn't take big gun to kill them. It just takes them a little longer to figure out they are dead and lie down. Elk aren't that hard to kill either. Some bullets designed for target shooting might not work well, but some will. If you're not sure, then don't go there. Any of the solid copper bullets will work well too, but they don't need to be as heavy. A 140 gr copper bullet will likely out penetrate a 175 gr lead bullet.
Some bullets are "hard" and don't expand rapidly, especially at slower impact speeds. Copper bullets are the hardest. But they penetrate very well, especially from bad angles. As long as impact speeds are up there they do still expand. Animals hit with them rarely drop in their tracks. but will die if you hit vitals.
Softer bullets expand very well and provide some shock value to put game down faster. They also expand well at longer ranges where they have slowed down making them a good long range bullet. But since they don't penetrate as well don't workl if you take shots from bad angles. You may have to pass up some shots until you get a clear broadside shot.
Pick your poison, both tactics work. Just don't pick a bullet and ask it to do a job it wasn't designed for. If you go with a softer bullet it is a good idea to go heavy for caliber in order to still get penetration. If using a hard bullet you don't need the weight for penetration and can use a lighter bullet. Which helps with expansion since it impacts faster.
I'd either use a 140-150 gr solid copper bullet, or any 160-175 gr jacketed lead bullet. I don't think manufacturer matters that much. Find what works best in your rifle.