The unique thing about this place that I find fascinating is the efforts of the Rosh yeshiva to consider Aristotle as a commentary of Plato and not as an adversary.
There was no denying that Aristotle disagreed with Plato on important points but still they sought insights into Plato by means of Aristotle.
What became of this? It became the pillar of all Western Thought. The Neo Platonic school of thought became the basis of Saadia Gaon, the Rambam (Maimonides), Crescas, Hegel, the Ari (Arizal, Isaac Luria), Augustine, Ibn Gavirol.
The reason I bring this up is that I think people have made too much of a big deal out of the arguments between Kant and Hegel. Way too much. What I see is a kind of learning of Kant that would use insights of Hegel to understand Kant much like the Neo Platonic, Plotinus, used Aristotle as a commentary of Plato.
I mention this because I have been troubled for a long time about what you would call intellectual intuition. This I think is at least one major difference between Kant and Hegel. And On this issue I definitely go with Kant. But I can not see why that would cancel the insights of Hegel.
I admit i am nervous about saying this because of my lack of knowledge. Still I see this as a promising approach.