We continue the study of exact Lagrangian fillings of Legendrian (2,n) torus links, as first initiated by Ekholm-Honda-Kalman and Pan. Our main result proves that for a decomposable exact Lagrangian filling described through a pinching sequence, there exists a unique weave filling in the same Hamiltonian isotopy class. As an application of this result we describe the orbital structure of the Kalman loop and give a combinatorial criteria to determine the orbit size of a filling. We first give a Floer-theoretic proof of the orbital structure, where an identity studied by Euler in the context of continued fractions makes a surprise appearance. This is followed by an alternative geometric proof of the orbital structure, obtained as a corollary of the main result. We conclude by giving a purely combinatorial description of the Kalman loop action on the fillings discussed above in terms of edge flips of triangulations.