plotting - How to make the mesh to rotate with a surface in Manipulate?

Here's a Manipulate code to show a particular 3D surface, rotating uniformly in time. The point of this Manipulate box is to show that the surface do indeed rotate like a solid, so I can't "cheat" with its evolution to get some better performance.

Manipulate[
SphericalPlot3D[
1/(16Pi)(8Cos[4(phi - t)]Sin[theta]^4 - 35 - 28Cos[2theta] - Cos[4theta]),

{theta, 0, Pi}, {phi, 0, 2 Pi},
ColorFunction -> Function[{x, y, z, theta, phi, r}, ColorData["Rainbow"][r]],
Mesh -> {18, 7},
PlotPoints -> {32, 24},
MaxRecursion -> ControlActive[0, 2],
PlotRange -> {{-1, 1}, {-1, 1}, {-1.5, 1.5}},
Boxed -> False,
Axes -> True,
AxesStyle -> Directive[RGBColor[0.50, 0.50, 0.90], Dashed],
AxesOrigin -> {0, 0, 0},

Ticks -> None,
PerformanceGoal -> "Quality",
SphericalRegion -> True,
Method -> {"RotationControl" -> "Globe"},
ImageSize -> {500, 500}
],
{{t, 0, Style["t", 10]},
    0, 2 Pi, 0.01,
    ImageSize -> Large,
    Appearance -> {"Labeled", "Open"},

    AnimationRate -> 8 Pi,
    DisplayAllSteps -> True}
]

Now, if you watch closely the animation, you'll see that the vertical subdivision grid do not rotate with the surface. It is fixed relative to the observer, and the mesh gets some deformations at some places while the surface rotate.

So how can I make the vertical lines to rotate with the surface ?