The rope cocker is a gret tool to prevent off center cocking, just make sure your clips are against the rail and not out any from the rail (just to make sure it does not stick out and pulll off center).

When shooing target heads, you should not get any wondering with the arrow. I know that the thunderheads have a stiff spine in the head so that the tip of the head should still be on the center of the axis. With cheaper heads and a soft spine in the head, it can become off center really easy. If the tip is off the arrow's center axis, it will also cause the arrow to wonder (with practice the spin test will help determine if it wobbles or not).

A spin test is spinning the arrow, point tip down (I use the palm of my hand) and look for a wobble where the head joins the arrow, but target heads should not get this anyway, so I do not think this is your problem.

Are you shooting just one arrow or alternating different arrows. Could be bad arrows, bent alumin. ect. If you are using more then one arrow, try your shooting with just one arrow to rule out bad arrows (get a group with one arrow, then get another group with another arrow).

Maybe someone else has a suggestion that might help.

Good luck.