No, you can't rechamber without having a bulge in the fired cases. The shoulder of the .243 is larger than the 6mm Remington is at the same point, so you would have, in effect, two chamber shoulders.
You could have the barrel set back and rechambered or the rifle rebarrelled, but, while I like the 6mm a lot, there is not enough difference (IMHO) to justify the cost of the work.
Given the same powder charge, same bullets, etc., there is not going to be any difference in barrel life. The main advantage of the 6mm is that the case can take a couple of grains more powder and can be loaded hotter, but that will certainly not be an advantage if you are looking for longer barrel life.
Jim