The paper by Felikson, Shapiro, and Tumarkin gives a complete classification of quivers of finite mutation type that don't arise from triangulations of marked surfaces. Existence of a maximal green sequences for the quivers in the mutation class of Dynkin E6, E7, and E8 was shown in Theorem 4.1 in the paper by Brüstle Dupont and Pérotin. The quivers in the mutation class of X7 were shown not to have a maximal green sequence by Seven.
Here we give a list of maximal green sequences for every quiver in the exceptional finite mutation classes. We use the convention given above in Brüstle Dupont and Pérotin for our maximal green sequences. The format of the files below is the index of the quiver in the mutation class as generated by the b_matrix_class() function in the ClusterSeed package of Sage by the initial quiver in the list. Then we give the corresponding skew-symmetric matrix of the quiver followed by a sequence of vertices that give a maximal green sequence for the quiver. We break the large mutation classes into several files for convenience.