Congratulations on the tag. I envy you! The unfortunate news is that you will develop scar tissue, adhesions, and definitely arthritis where you had surgery. I'm not a fan of having anything pounding away on a newly modified body part personally. The best advice I read so far is learning to shoot with the other eye/shoulder, especially if your vision is just as good in that eye. That was my first thought when I opened the thread.
Pain free doesn't = "healed" just as healed doesn't = "pain free."
With a well placed shot, there's no reason the 243 won't do the job. That said, I'm no fan of that caliber. Since it looks like you are taking a 7-08, I think that is a great choice. Even if you are shooting it and can handle the recoil, I don't recommend the continued jarring on the shoulder. Ultimately, that's between you and your surgeon. Maybe you can adapt to a shooting vest with a pad in it.
Possessing a once in a lifetime tag and potentially worsening a shoulder further is a tough choice. Good luck and good hunting!