Nothing wrong with the 270 for deer 2400ftlbs energy!+ The beest bet is a little lower to take out the heart or top of heart /bottom of lungs, deer will definitely die in 30 mins you did the right thing with the deer waiting for it to die etc. I had one exact same some years ago, 90 yd free hand shot deer exited left ( literally ) on its chest and back legs, went over a berm and into the trees. I hung around for 20minutes and then went quietly forward and luckily spotted it lay down under some pines, I head shot it from where I was about 50-60 yds and it was over. When I got to it, the reason was obvious, I had shot a bit low, the bullet broke nearest leg went through the bottom of the chest below the heart and broke the other leg. It would have lasted many hours even a few days as there was no real bleeding, so I was glad I got a second chance, but I bet yours was similar. The only thing I could say if that happened again , give it a mercy shot, I surely will if it happens again. But if you think about it, you were just unlucky and the heart lung shot is till the best. The area for fatal wounding is five times greater than a head / neck shot and as anyone will tell you a deer can move far faster than you can and it can and will move between you pulling the trigger and the bullet getting there, so you end up wounding or blowing its jaw off or something. Not many of us would rest easy knowing a deer has gone off to die in agony over many days! The hard bit is taking the time to look at the deers position and deciding whether to aim in front or behind the foreleg. If it is just standing behind, but if it is feeding and walking in front may be best.
Second deer , 2-300 yds run for a lung shot is not unusual, as the deer literally runs out of oxygen in the blood then drops, smaller deer about 100-150 yds often. They are findable and I would call those good shots, Ive had a deer with no heart go 70yds because it had seen me as I shot and the adrenaline keeps them going.
I wouldn't get too wound up about drop on the spot kills they are good if it happens but the others are legitimate shots and as above much more certain to kill in the engine bay, than going for tricky head/neck shots. IMHO
Better the man suspected of being a fool keep his mouth shut, than to open it and remove all doubt.