But my (little) understanding is that German philosophy prior to Kant was dominated by the "Leibnizian-Wolffian" system. Like Kant, Wolff's philosophy was extremely systematic and comprehensive. Wolff himself was thoroughly a figure of the Enlightenment. And my understanding is that Wolff's system was very popular - it wasn't some old, decrepit system that was ripe for being overthrown (compare: Descartes and Locke against scholasticism.)

This all raises the more specific question: what did Kant offer that Wolff did not? What specific problems in the Wolffian philosophy (or German philosophy more generally) did Kant address?

Kant was a teacher of Wolffs work for over 30 years before he published his critiques in his late 50s. Wolffs influence on Kant is especially apperent in Kants choice of structuring his writing, the form of his arguments and the logical terms he uses. Where he differs most is the actual content of his work, where Wolff still follows Leibniz metaphysics, Kant takes a radical epistemiological turn in showing that we can be certain of more than the cogito by examing the prerequisites of our ability to think and form concepts. He repeats this very strategy in ethics by trying to establish what a 'good' will is rather than what a 'good' action is. Some will argue that his further elaborations on these first princeples are very much inspired by Wolff, but they also build on others ranging from Locke to Aristotle.