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I probably want to edit my state directly, but I'm not sure how to do that.

@clever-address-74879 excellent solution, another method of recovering would be to use the alias resource option (https://www.pulumi.com/docs/intro/concepts/resources/options/aliases/) to tell Pulumi that the resource changed name, this may have worked:

var zone = new Zone("new-name-for-zone", /* args */,
    new CustomResourceOptions { Aliases = { new Alias { Name = "Calling [ToString] on an [Output<T>] is not supported."} } });