Statistic that is responsive to changes in time series, yet not too volatile
Hi: I don't think that there are general statements that can be made because the median component used in the second approach is pretty ad-hoc.

You probably already know this but the $\alpha$ that you defined for the EWMA is such that your EWMA has the same weighted age as just taking a moving average of length "window". Therefore, if you an moving average of length window and an EWMA with parameter $alpha = \frac{2}{window + 1)$, they will look quite similar.

The way you look at things in terms of "reaction time" till convergence or catching up is interesting.

The standard approach for this ( and more systematized but I'm not critcizing your creative approach ) is to just use an ewma with parameter $\alpha$.
The different values of $\alpha$ chosen will equate to the half life of an impulse response for $S_t$. So, just by plotting the impulse response, you can see what $\alpha$ you prefer.

So, for example, suppose you used the EWMA with parameter $\alpha$. ( $\alpha$ is between zero and one for invertibility purposes ) Therefore,
your exponentially smoothed value, $\hat{S}_{t}$, at every time step, $t$ would be:

$\hat{S}_t = \alpha \times \hat{S}_{t-1} + (1-\alpha) \times X_{t} $.

Now,  we assume that $S_{0} =1 $ and $X_{t} = 0 $ for $t$ greater than zero and that we start start smoothing $S$ at $t=1$. So, since  the halflife corresponds to the period when $\hat{S}_t$ becomes half of what it was originally, this corresponds to 

$\hat{S}_{halflife} = \frac{1}{2}$.

Therefore, we have $\frac{1}{2} = \alpha^{halflife} $.

Taking the log of both sides gives $halflife = \frac{log(1/2)}{log(\alpha)}$.

So, the point is that, given the impulse response at time $t=0$, then different $\alpha$ correspond to different halflives 
for the response and you can play around with the halflife to see what works best for your problem. 

Finally, if this was obvious or you were already familiar with it, my apologies. Also, IMHO, the best textbook exposition of this is Brown's "Smoothing, Forecasting and Prediction of Discrete Time Series". There are used versions on Amazon that are pretty cheap.