SSH.NET real-time command output monitoring

There is a long running script script.sh on a remote Linux machine. I need to start it and monitor it's activity in real time. The script during it's activity may output to stdout and stderr. I am searching for a way to capture both of the streams.

I use Renci SSH.NET to upload script.sh and start it, so it would be great to see a solution bounded to this library. In my mind the perfect solution is the new method:

var realTimeScreen= ...;

var commandExecutionStatus = sshClient.RunCommandAsync(
    command: './script.sh',
    stdoutEventHandler: stdoutString => realTimeScreen.UpdateStdout(stdString)
    stderrEventHandler: stderrString => realTimeScreen.UpdateStderr(stderrString));
...
commandExecutionStatus.ContinueWith(monitoringTask =>
{
    if (monitoringTask.Completed)
    {
        realTimeScreen.Finish();
    }
});

So, here is the solution I came up with. Of course, it can be improved, so it is open to critique.
I used

await Dispatcher.Yield(DispatcherPriority.ApplicationIdle);

instead of Task.Yield() because Task.Yield() will make continuation a higher priority than GUI events, but, as a bad consequence, it demands your application to use WindowsBase.dll.

public static class SshCommandExtensions
{
    public static async Task ExecuteAsync(
        this SshCommand sshCommand,
        IProgress<ScriptOutputLine> progress,
        CancellationToken cancellationToken)
    {
        var asyncResult = sshCommand.BeginExecute();
        var stdoutStreamReader = new StreamReader(sshCommand.OutputStream);
        var stderrStreamReader = new StreamReader(sshCommand.ExtendedOutputStream);

        while (!asyncResult.IsCompleted)
        {
            await CheckOutputAndReportProgress(
                sshCommand,
                stdoutStreamReader,
                stderrStreamReader,
                progress,
                cancellationToken);

            await Dispatcher.Yield(DispatcherPriority.ApplicationIdle);
        }

        sshCommand.EndExecute(asyncResult);

        await CheckOutputAndReportProgress(
            sshCommand,
            stdoutStreamReader,
            stderrStreamReader,
            progress,
            cancellationToken);
    }

    private static async Task CheckOutputAndReportProgress(
        SshCommand sshCommand,
        TextReader stdoutStreamReader,
        TextReader stderrStreamReader,
        IProgress<ScriptOutputLine> progress,
        CancellationToken cancellationToken)
    {
        if (cancellationToken.IsCancellationRequested)
        {
            sshCommand.CancelAsync();
        }
        cancellationToken.ThrowIfCancellationRequested();

        await CheckStdoutAndReportProgressAsync(stdoutStreamReader, progress);
        await CheckStderrAndReportProgressAsync(stderrStreamReader, progress);
    }

    private static async Task CheckStdoutAndReportProgressAsync(
        TextReader stdoutStreamReader,
        IProgress<ScriptOutputLine> stdoutProgress)
    {
        var stdoutLine = await stdoutStreamReader.ReadToEndAsync();

        if (!string.IsNullOrEmpty(stdoutLine))
        {
            stdoutProgress.Report(new ScriptOutputLine(
                line: stdoutLine,
                isErrorLine: false));
        }
    }

    private static async Task CheckStderrAndReportProgressAsync(
        TextReader stderrStreamReader,
        IProgress<ScriptOutputLine> stderrProgress)
    {
        var stderrLine = await stderrStreamReader.ReadToEndAsync();

        if (!string.IsNullOrEmpty(stderrLine))
        {
            stderrProgress.Report(new ScriptOutputLine(
                line: stderrLine,
                isErrorLine: true));
        }
    }
}

public class ScriptOutputLine
{
    public ScriptOutputLine(string line, bool isErrorLine)
    {
        Line = line;
        IsErrorLine = isErrorLine;
    }

    public string Line { get; private set; }

    public bool IsErrorLine { get; private set; }
}