I dont want to come across as condescending or anything but are the horses on the property used to gunfire? 150 acres is not a huge block of land, a .243 with a shortened barrel is going to be bloody loud, last time I heard of someone shooting on a small horse property it got costly in vet bills as fences and horse flesh dont go well together, I'd also be wary of what happens when a projectile goes straight through a soft spot of a dog and keeps on going, baring in mind a .243 is still breaking the sound barrier at 800 meters it keeps going for a lot longer, do you have a bit of high ground or a tree hide to shoot from to ensure a downwards shot?
You also mention that the neighbours are happy/not fazed with the feral animal problem? have you spoken to them about your intention to deal with the issue? do they also have livestock that could be spooked by the sound of gun fire? are they the sort of people that are going to call the police and say that your shots were "wizzing past their house", I know it sounds silly but it happened to a mate of mine who was shooting Indian minor birds and rabbits with an air rifle on his 50 acre property and the police came to check,
Don't get me wrong, I have my licence and own a few bang sticks, I'm ex military myself and more than happy to go away shooting pests and dabble with the long range target shooting, but as the climate around Firearms gets hotter I hate to see people get into trouble needlessly, even if its short lived and get cleared of any wrong doing,
If your really set on shooting on the property then the suggestion of .300 blk wasn't a bad one in my opinion, there are not a huge amount of calibers that you can buy factory subsonic ammunition for and it makes a huge difference in noise levels, if your getting a .22 or know someone with one, go buy some subs, standard velocity and high velocity ammunition, compare the difference in loudness and then think what its going to be magnified by 20 for your .243, also shoot the .22 close to the horses and see how they react to that before letting a 12g or 243 off around them.
the other option is find a licensed pest controller that can use suppressed firearms and get them out to deal with the pests.