Hey!

I don't think there's much difference between standard predictive modeling and sythetic controls. Whatever leads to the best bias-variance and generalizes well.

PCA has been used and seems like a logical choice. Normalizing should work because we're using linear transformations - standarization, on the other hand, would change the distribution and thereby distort variables.

Beyond that, I think a good understanding of toic is important. Making sure that you include variabels that should have casual relationships to your y-variable is important. If you put correlational variables (that don't have the ability to generalize by means of a causal relationship) into PCA, you'll get bad results and won't be able to debug.

Hope this helps!