Well, campden doesn't kill yeast. Winemakers use it all the time as a preservative/antioxidant. If you use enough campden to kill the yeast, the cider will be undrinkably bad.
Most wine and cider makers use sorbate if they want to sweeten a batch. Sorbate doesn't kill yeast either, but it keeps it from reproducing. It works better in the presence of sulfite (campden) so they are added together.
The problem with adding sorbate in your scenario is that it doesn't kill the yeast, but keeps it from reproducing. Since there would be plenty of yeast in there, from eating the priming sugar, the sorbate would be ineffective.
A sweet carbonated cider is very tricky to make unless you're experienced with it.
You can use non-fermentable sweetners like lactose or splenda and then prime the bottles if you want. Or you can bottle pasteurize according to the sticky on the forum.
I'm a fan of still dry wines, meads, and ciders, so I have very little experience with pasteurizing.