A 243 is not incompetent on deer by any means.
your impact velocity is not so high.
A bullet that expands very rapidly in the first two inches, but still holds together through exit is what you need. "24 inches of penetration" isn't helping you if the bullet opens at 6 or 8 in. You've lost much of your opportunity to cause trauma at that point. It's ironic but some of the less expensive cup and core bullets outperform others as the velocities decrease. That's why I roll my eyes when I hear people trying to shoot 180 coppers out of a 308. They missed the whole strategy. If you can get a standard game King out the barrel at 2700 ft per second it's a pretty incredible performer. If you want deer to drop right away it's important that you use one that opens very rapidly, at the range and velocity you intend to make contact.
Obviously a 308 carries a lot more energy and potential tissue damage than a 243. But I think matching bullet performance to the game and impact velocity makes more difference.
Don't mean to start another pissing match but I'm a high shoulder shooter too. My deer don't run.
In actual numbers seven of my last 100 dear moved more than 20 ft. Of the three I lost, on two I was unable to make a high shoulder shot due to shot presentation and one was because the bullet failed to open up at 200 yards. I retested that same bullet the next week on another deer at the same range and got the same result. But I recovered that one. And then I used a GPS app to make a geo.circle, and found the remains of the first year I lost. And I will not use that bullet again on dear.
So 7 mm 08 or 308 will be more lethal at the yardage you mention, what other factors are quite possibly more important.