Don't know what resources might be available to you or how much trouble you are willing to go to for this project. A few thoughts...
Rusting is the combining of oxygen with iron to form iron oxide. The presence of oxygen is required. Coatings, such as the wax dip suggested above, serve to keep oxygen away from the article to be protected.
Otherwise, the air in an air tight container holding the rounds might be replaced with an inert gas, like nitrogen or carbon dioxide. Or the oxygen can be extracted from inside the container, by using a vacuum pump to remove the oxygen containing atmosphere. Even if the oxygen inside the cases were to leak out, the cartridges will still work. External oxygen is not necessary for the powder to work. The powder, nitrogylcerine and nitrocellulose, rapidly decomposes rather than "burns".
Desiccants, drying agents like silicon dioxide remove water vapor, which accelerates oxidation, but will not prevent it. Oxygen is still present. Still, storage in an air tight container (containing air) will allow only a limited amount of oxygen to contact that which you are trying to protect.
One other idea, is to use the treated paper that tool makers and machinists use to wrap steel parts. Not sure where to get it, or how it works, but it smells like camphor. You could wrap your packages with it and store them in airtight containers. Not as good as a vacuum, but better than nothing.
Not sure how long you plan to try to preserve your cartridges, but they will have a finite working life span. The the propellants will eventually degrade and the so will the priming compound. It is generally thought that the old, corrosive primers are more stable over time than the newer non-corrosive types. Still, the working expectation is for multiple decades. Will your stash work for your great-grandchildren? No one knows.
Oh yes. Consider that the inside of your cases can rust as well from the nitrates in the powder and the air inside the case. A little bit, anyway. The rounds will still function as long as the primers still work.