I talked to my Dad OP and he said he uses 36 grains of IMR 4320 with a 100 grain bullet. Its been his standard load for years and years. He said he never had a deer get away with it. He said he loaded the same load for my Grandfather and I know he killed a lot of deer, hogs and turkeys with his Remington 700 .243. I also remember about thirty years ago using one of my Father's .243s to shoot a doe, it ran about 20 yards after a behind the shoulder shot.
IMR website shows 37.6 as max with an 85 grain projectile so it should be safe. The load he used that he shot the really tight groups with was 37 grains of 4320 and a 75 grain Sierra. Looks like from this thread that there are some good loads for the .243 Winchester with many of the most popular rifle powders OP and now you have one more idea.
PS: IMR website shows 42 grains of 4350 as Max, so approach those Handloads.com loads with caution, if at all.
"No free man shall ever be debarred the use of arms."- Thomas Jefferson