As you have seen, and I have found as well, the OAL of the bullet can have a very large effect on a cartridges accuracy. Every time I begin loading for a rifle for accuracy, I make up a case for my stoney point gauge. This allows me to see the max OAL for any given bullet in that guns chamber. I like my bullets 5-7 thousands off the rifling. BUT BEWARE, if you are the lazy sort, who doesn't keep his guns chambers clean this could cause problems.
The 243 has been on my wish list, in a Handi for far too long!!! I would go for the Ultra Hunter 22"or Varmint 24" both in a heaver contour.
Good luck with it!!
CW