It's doable, but you'd need to do it in a few stages.
The cheapest way is to buy the Lee Cast Bullet Sizer die (actually, a series of them, in your case). This unit retails for about $25 for certain factory standard diameters, and Lee will custom make them for you in whatever diameter you want for a few extra bucks.
For example, a few years ago, I had a rifle with a .309 barrel. I just bought one of these standard Lee sizers in .309 and ran some ordinary Horanady .312 bullets made for the .303 British into them on my reloading press. In one pass (with my cheap Lee press), the bullets were done, and were very nicely uniform.
The key is that you can only go about .003 at a time.
I've often wondered what it would be like to size down some 8mm bullets (.323) to the actual diameter of most .303 British barrels -- .314. To do that, you'd need to special order a .320 sizer and a .317 sizer. Lee makes a .314 sizer as a factory option. After running the bullet through those three dies, the total "shrinkage" would be .009".
Many people have suggested that this might be too much. A bullet can only be sized down so much and then the jacket springs back a tiny bit, leaving a gap because the lead core stays sized down. This would not be good for accuracy. I'm not sure whether .009" would cross the threshold, but it would be close. You going from .323 down to .308 would probably cause some jacket spring back.
But, you may still have options. Most miltary FMJ bullets have a hollow base. The significance of this is that even if your jacket springs away from the core a bit after sizing, the blast of firing on that open base would theoretically push the lead back up into close contact with the jacket again, just like the 19th-century Minnie bullet. Another possible option would be to use one of the modern bonded-core bullets.
All of this is currently theoretical in my mind, however. I've never actually tried this, but I plan to some day.
Another source for your bullet sizing die is the following:
http://www.ch4d.com/catalog/?p=89
This is basically the same thing as the Lee Cast Bullet Size die, but a little more expensive. (Even thought the Lee die is called a "Cast Bullet" size die, it still seems to work with jacketed bullets.)
I've discussed bullet sizing with the CH guys via email, and they seem to think it works OK if done in stages.