Well, I discovered that RCBS has closed their custom shop earlier this year, so I went to Lee and asked them to make me a die to draw .224 bullets down to .223. $38 (plus postage) later, it arrived on Saturday. It came with the die, push rod that clips into the shell holder, a bottle of Alox and a storage container that also serves to collect the resized bullets.
I set it up per the instructions, lubed up a Sierra 40 grain .224 jacketed soft point bullet with Hornady Unique and pushed it through the die. It went through with surprisingly little effort. So little effort that I started to worry that Lee had sent me a .224 die and not a .223 die, but that worry was short-lived. Lee had done everything they promised.
The push rod pushes the bullet through the die but not out of the die. It appears that subsequent bullets are supposed to do that. Since I only had the one test bullet, I pushed it would with a pin punch. There was no resistance to hand pressure, just enough that it wouldn't fall out of the die when I unscrewed it and turned it upside down.
The body of the bullet indeed bore the marks of having been worked by the die. My digital caliper gave inconsistent readings, but the micrometer doesn't lie. The bullets came out of the die .2230 at the point where the ogive met the body. The body gradually increased in diameter until at the base it was about .2236. Since the consensus of the two gunsmiths who slugged the chamber and barrel was that it was "about .2235, this should work fine.
I'll come back and "ressurect" this thread when I get a chance to test a loaded round using both the factory .223 bullets and the drawn .223n bullets.
But, in response to my own questions - some of which have already been answered by others in very helpful posts - jacketed bullets can be put through a die and successfully resized to a smaller diameter. The resized bullet doesn't appear to have been damaged in any way and the jacket still seems to be firmly attached to the lead core.