Make contour lines level with graph interval?

data = Table[Sin[j^2 + i], {i, 0, Pi, 0.1}, {j, 0, Pi, 0.1}];
zmesh = {-1/3, 0, 1/3};
facegrids =  Thread[{Join[#, -#] &@IdentityMatrix[3], {Range[5, 30, 5], zmesh}}, List, 1];

ListPlot3D[data, MeshFunctions -> {#3 &}, Mesh -> {zmesh},
 FaceGrids -> facegrids, BoxRatios -> {1, 1, 1/2},  PlotRangePadding -> 0]