Consider a simple algebraic group G of classical type and its Lie algebra g. Let F be an algebraically closed field of characteristic p>> 0, we write g_F for the F-form of g. Let U^{\chi}_{F, \lambda} be the central reduction of U(g_F) with respect to a pair \lambda\in \mathfrak{h}^*/W and \chi\in \mathfrak{g}^{*}_\mathbb{F}^{(1)}. We focus on the case where \lambda is integral regular and \chi is nilpotent. In [BM12], there exists an algebra A^{0}_e (the fiber of the noncommutative Springer resolution over a nilpotent element e\in g) equipped with an isomorphism K_0(U^{\chi}_{F, \lambda}- mod)\cong K_0(A^{0}_e-mod)$. This isomorphism sends classes of simple modules to classes of simple modules. Let Y_e be the set of simple modules of A^{0}_e. Let Q_e be the reductive part of the centralizer of e in G. As Q_e acts on A^{0}_e by algebra automorphisms, the finite set Y_e has the structure of a Q_e-centrally extended set. In this work, we study this centrally extended structure of Y_e when the partition of e has few rows. In particular, we first prove that Y_e can be determined by certain numerical invariants of the Springer fiber B_e. Next, we introduce a variety B_e^{gr} \subset B_e that shares the same set of numerical invariants as B_e. We then reconstruct Y_e from B_e^{gr} using categorical tools. The main result is that the derived category D^b(B_e^{gr}) admits a complete exceptional collection that is compatible with the Q_e-action. The objects in this collection can be regarded as the points of Y_e in a suitable sense. As applications, we obtain an algorithm to compute the multiplicities of orbits in Y_e, which provides some numerical information on cells in affine Weyl group.