First Elk I shot would have been around 1972, few more including moose over the next 40 years after that, Cup and core bullets from a 303 brit were more than enough in the beginning, I have shot Elk and moose (two grizzly and numerus Black bears) with 270, 30-06, 300 win and Weatherby, 338 man and 45-70, been reloading since 1977 so I have also tried every bullet manufacture I could buy bullets from. Barnes -x when they first come out was a favorite and a old stand by Nosler partition.
But, no bullet killed any Elk deader than my old 303 brit with 180 gr cup and core, CIL, Imperial Saber tip, Rem corelokt, or silver tips.....terminal ballistics is not as complicated as people and bullet manufactures sales reps try to make it out to be, punch a hole in the lungs and the Animal is dead, maybe not bang-flop like struck by lightning, but still dead! what hurt cup in core bullets was trying to drive them too fast for bullet weight, keep the "impact" velocity under 2700fps and they work fine.
shot placement is key, a gut shot animal with a 375HH TTSX will still go a long long way, gut shot is gut shot with any bullet, practice shooting before you try an animal at 500- 600 yards , no shooting sticks, no bi-pod, shoot off hand, kneeling and prone, no sand bags, or cement shooting tables in the bush on on the side of a mountain, once you cant hit a milk jug full of water constantly, you met you limit. (most will have met that limit under 100 yards!!)