For me …..an easy answer!
Some of the frangible bullets offer rather impressive kills with shots through the lungs!
The "fly in the ointment" with this philosophy is…..the bullet must get to the lungs! Thus enters that nasty thing called "REALITY"!
If you have faith that the stars will align perfectly for you, the elk standing broadside, and the bullet "surgically" placed by you…..this is no place for a fragile/frangible bullet.
You want a bullet that is designed for hunting…..a bullet designed reliably expand within it's operating velocity range, that "WILL NOT" fragment, retaining near 100% of it's original weight. Meaning, this bullet will penetrate deeply through bone and dense muscle, getting to and damaging the vitals ….if it had less than perfect placement.
My choice would be the Barnes 80 grain TTSX. memtb