The heaviest the 1-12" will stabilize well, as a rule, is 55 grains. Above that and your mileage will vary. It also depends on what velocity you load into them. If you take a 60 and back down the velocity you might get it to stabilize and shoot accurately. But then you trade off FT/LBs. And more important than that is the velocity the bullet was designed for. If the bullet was designed to expand at velocities between 2400 - 3600fps when hitting the target and you send it down range at 2200fps the bullet won't perform correctly when it hits it's target. It may not penetrate the required amount or it may not expand and overpenetrate and pass through like a FMJ.
So there's alot of things to look at besides twist and bullet weight, you also have to include bullet construction, design, and velocity.
Stuff you probably already know.
You might also look into Noslers 55 grain bullet offerings. I was thinking there was a 55 grain partition, but maybe i'm wrong.
I also know of people using Remington 55 grain PSP's with good luck on small deer and the close ranges you were talking about.
As versital as the .224 bullet selection is I'm sure you can find something your handi likes, just shoot withen the 223's limitations and your limitations and you'll be successful. Just like bow hunting, know your bow limitations and know your limitations. If you don't know them both when you're ready to go hunting go to the range instead. I've heard this with from many bow hunters and it should hold true of all hunters no matter what the game or weapon.
later,
scruffy