Practically handling many non-stationary forecasting predictors This question is about specific strategies to deal with non-stationary variables in forecasting. 
This problem usually rears its ugly head when you have a predictor whose levels are relevant to the response, but whose first difference carries very different information. Generally, if there is one or two of these in my model, it suffices to use intercept dummies that are one when the nonstationary levels predictor is 'high'. Similarly, it can sometimes suffice to interact these dummies with various other predictors so I don't have to have the nonstationary variable as a regressor. 
But what if I have 15-20 of these nonstationary predictors whose levels are all highly relevant to the response? For example, consumer demand being 'high' may be critically relevant to the model; by first differencing I can't incorporate this information into my model anymore. Now consider the case where there are 15-20 other similar variables where the level is critical.
What is a sophisticated strategy to dealing with this other than using silly amounts of dummy variables, chucking it into a statistical learning algorithm, or chucking them all down the bin? 
Perhaps this problem requires a traditional machine learning solution? Something like random forests make sense, but I am looking to keep the number of parameters down since the speed at which I can get forecasts out of the model is important. 

To given an example of where levels are important and can't be capture by first differences, look at the following example predictor in R:
plot(sin(1:400/50)+sin(1:400),type='l')
What's important to my $Y$ is if this predictor is near a peak versus the opposite case of being near a trough. But there is no way to integrate this information into my model by using the first difference of this predictor. 
 A: In general, you could look into the concepts and models of "co-integration" and "conditional heteroskedasticity".
In the case where the response appears also non-stationary, then you should look whether it is co-integrated with the regressors (you didn't mention co-integration at all in your question). In a nutshell, co-integration exists when the response $y_t$ and the regressors $\mathbf X_t$ are non-stationary, but there exists a co-integrating vector that creates a linear relationship between them that is stationary (or "integrated of order zero")
$$y_t -\mathbf X_t\beta = u_t, \qquad u_t = I(0)$$
If this is the case, a regression in levels can produce reasonable inference and forecasting results.
Another way to approach the possibility of a non-stationary response, is the "conditional heteroskedasticity" approach models. There are too many variants to discuss them here. The essence is that the variance of the process is not constant but depends on the regressors and/or its own past (the "auto-regressive" version). 
Let's consider now the case where the response is stationary. Here, before discussing statistical methods, we have to deal with the conceptual problem that arises: how can it be that a stationary response depends or co-varies with a non-stationary regressor?
The response being stationary, it has a constant mean, i.e. it has an attractor around which its realizations happen. If a regressor is "trend-stationary" (i.e. non-stationary due to the existence of a deterministic time trend), it is difficult to envision that a regressor that continuously rises or falls with each realization, has something to offer in explaining the variation in a process that has constant mean.  
Assume now that the regressor is non-stationary in the mean because it exhibits cyclicality (like a trigonometric function). In that case, we could argue that it may influence the seasonality that may be present in the response: this is essentially a way to rationalize the method you described, i.e. turning the quantitative information into qualitative information ("low/high") and use dummy variables. You can increase the level of sophistication here by looking into "seasonally co-integrated" variables and the associated methods.
A final note: it is important to try to determine whether non-stationarity refers to both the mean and (co)variance of a process, or only to its variance, or only to its mean. Each such scenario has different issues to deal with in applied work.
