I love the 243 you should be able to make it shoot good enough to kill them at 350yards.I have a stock rem. 700 sps that I bought for my little girl,I have done a trigger job on it,it shoots MOA groups with the right bullets.It likes fed fusion 95gr.and loves hornady 58gr. there just not big enough for deer.But they have enough energy for a songdog as far as you can hit him.I dont know your gunsmithing ability's but make sure the barrel is floated not touching the stock,until you get to the receiver,and scrub that bore good fouling can kill a rifles accuracy,in my opinion you already have one of the best calibers,the 243 was one of original short action magnums.As for the 240 weatherby have you priced ammo for if you dont reload they can be pretty high.