I'm not as old as many on this forum, but I have been hunting elk for 29 years. I have killed my share of elk, not sure of an exact tally and most were taken with a bow. However, I have killed a few with firearms. I have used 270 winchester, 7mmbr, 475 wildey, 300wsm, 45-70, 405 winchester. I have been with others who have used 338 win mag, 300wsm, 270.
I have also killed a few moose, a few caribou, moutain goat, bighorn sheep, antelope, a few bears, quite a few mule deer, and a few whitetails.
One thing I can say with certainy is that NO animal ever hit through the chest with both lungs and or heart shot, ever ran more than around 150 yards, the vast majority never running more than 80. The only times I saw an animal make it any real distance were shots that got only one lung, or barely nicked the lungs or were far back and actually got liver.
My 7mmbr xp100 has taken more elk than any other of the firearms I have used. 130gr bullet at around 2300fps IIRC.
But, if you want a bullet to kill them instantly with a Texas heart shot, use something big.