I used to make 06 brass into .44 automag pistol brass. The process of changing calibers using a parent case is not that difficult, but is a PITA.
Going to the .243 is going to leave you with headstamps of a .308. If you don't own a .308 the confusion factor won't be an issue, but if you do, proceed with caution when storing rounds.
Some say to lube the heck out of the outside and inside the neck and use a standard .243 sizing die. Be aware the neck getting squeezed might cause excess thickness, and neck turning might be in order. Reamers are available from Midway or Brownells.
I recommend Brownells as using our link on the home page doesn't save you any money, but gives BS a referral reward that helps us keep the site running.
The major die manufacturers sell resizing dies to do what you want, but I'd try a few cases using normal .243 dies, and measure them against a factory .243 brass. Do what you have to do to mimic the factory brass.
Annealing the brass might be something one needs to do as well. Try it first without annealing, and you will get an idea if its necessary.
Later,
