The other big consideration at a range of 300 plus is the terminal impact velocity, energy, bullet expansion and wound channel.
At a range of 100 your impact velocity will be well above 2000 fps with plenty of energy. The bullet will expand well and you will have a good permanent and temporary wound channel. The temporary channel is key as this is the shock wave that will go several inches either side of the bullet path. In a roe deer this shock wave will have a major impact on all the vital organs, in particular the CNS knocking it unconscious. With a red deer, they have a much larger boiler room, but the shock wave will still affect other organs well beyond the path of the bullet. This results in a quick kill.
Out at 300 plus you much more relying on just the permanent wound channel without much shock wave and temporary cavity. This means that to get a quick clean you need even more precise in your point of impact and shot direction. At 300 most cartridges will have lost a good proportion of their velocity and energy leading to less certain expansion and small permanent and temporary wound channels.
If you can hold a 4” group on a range where you have time to get everything set up perfectly, this will easily open up to 6 or 8” group when in the field. Add in some elevation, wind, excitement and less than perfect set up the ability to precisely hit the target diminishes rapidly. And if you don’t hit it precisely, you don’t have the bullet energy to back you up.
Next course of events is to go and buy a 300 win mag with all its attendant costs and recoil.
Much better is to get in closer and reduce the ****up Coefficient considerably.
The ****up Coefficient goes up exponentially with range and doubles every 50 to 100 yards or metres.
We all make mistakes. The biggest mistake is not recognise them. Pressure to achieve cull targets is huge. However I am pretty confident that its better not to shoot at something a bit far. Either get closer or go and find something else. And you won’t waste a huge amount of time following up wounded or missed animals.