Aside from not using the dishwasher, how do I stop my silverware from rusting contained by the dishwasher? ...
Answers: Your silverware should not be rusting. It should be made out of stainless steel, which will not rust.
For those pieces of silverware that have a few non-stainless bit on them (like screws on the handle of paring knives), I'd simply do them by hand.
But do spend a couple of bucks to replace your silverware next to something that doesn't rust.
Or do all your silverware by appendage.
Or dry them as soon as the dishwasher is finished with its cycle.
After the washer shuts bad, immediately remove the silverware and dry it.