I don't have a .243 Win, i have a 6mm Remington, which, from a deer's point of view, is the same.
I shot 4 deer with this rifle.
1. Hornady 95 grain SST bullet, loaded to max of chart with IMR 4350, very fast, 3000 fps or so, lung and heart shot from 40 yards, no exit wound, i lost the bullet when i gutted the deer. Deer ran 30 yards and died.
Deer 2,3,4 were shot with the Hornady RN 100 grain semiroundnose bullet. This, loaded soft, at the low end of the scale with IMR 4350, about 2700 fps. Deer were
1. Shot in the neck, dropped dead, 1.5 exit hole
2. Shot in the lungs, a bit too far behind close to the diaphragm, lots of blood on the trail, deer ran 20 yards and died. 1/2" inch exit wound, but there were 4" holes in the rib cage under the skin. Lots of blood everywhere on leaves.
3.Shot high in lungs under the spine, angling downward. Deer dropped on the spot and died quicly. 1 inch exit hole in hide, 4-5 inch holes in rib cage, blood spattered by the shot everywhere, even 10 ft away from deer.
The .243 and the 6mm kill very well. You don't need a blood trail for them. It may be that the spitzer bullets shot by .243 were too soft and flying too fast, failing to exit.