You can send every item to republish via CoreService. You can user in your publish instruction ResolvePurpose.RePublish It can be something like this:

 private PublishInstructionData publishInstructionData = new PublishInstructionData()
    {
        ResolveInstruction = new ResolveInstructionData()
        {
            Purpose = ResolvePurpose.Publish,
        },
        RenderInstruction = new RenderInstructionData(),
        MaximumNumberOfRenderFailures = 10000,
    };

If you want to integrate this in GUI, you can always create GUI Extension that will execute this piece of code.

You can send every item to republish via CoreService. You can user in your publish instruction ResolvePurpose.RePublish It can be something like this:

 private PublishInstructionData publishInstructionData = new PublishInstructionData()
    {
        ResolveInstruction = new ResolveInstructionData()
        {
            Purpose = ResolvePurpose.RePublish
        },
        RenderInstruction = new RenderInstructionData(),
    };

If you want to integrate this in GUI, you can always create GUI Extension that will execute this piece of code.