Here is my advice based on a fair bit of elk experience. My family and friends have taken more than 70 elk on our hunts. All kills have been recorded. The most common cartridges used have been .270, .308, and 30-06. Some have been taken with 7mm-08, some with .375H&H. And most everything in-between. They all work when shot well and with good bullets.
If you are a competent hunter and not just a shooter, there is seldom any reason to take a shot over 300 yards. When we find a distant elk, we stalk closer. We have wounded and lost very few elk, but the four I can recall were a calf shot in the leg with a .308, a bull hit in the hump with a 30-06, a bull hit in the guts with a 300 magnum ( at about 350 yards! ) , and another bull gut shot with a 35 Whelen. A relatively "big" rifle doesn't guarantee a clean kill, good stalking, and good shooting with good bullets does.
An elk won't drop at the shot like a deer or even like some moose will. They often run hard and may show no sign of a hit. Always reload immediately after shooting. If you know you hit the first shot keep shooting at the running elk!
You already have two good elk rifles. Just don't use light and fast expanding deer bullets in them. Or buy a .300 mag, or a .35 Whelen, .338 or 9.3x62. All are excellent if you practise with them and can handle the higher recoil and still hit what you aim at from hunting positions. Don't try "iffy" shots, and place your bullets in vital organs. Hunt hard, stalk close, shoot well, and you will be successful. Have fun!