OK, not done this before but can get us started.
Using this Snippet, I changed the add_action and added an additional one with a different hook (__footer)
Try this and see if it helps.
//we hook the code on the wp_head hook, this way it will be executed before any html rendering.
add_action ( 'wp_head' , 'move_my_slider');
function move_my_slider() {
//we unhook the slider
remove_action( '__after_header' , array( TC_slider::$instance , 'tc_slider_display' ));
//we re-hook the slider. Check the priority here : set to 0 to be the first in the list of different actions hooked to this hook
add_action( '__header' , array( TC_slider::$instance , 'tc_slider_display' ), 0);
add_action( '__footer' , array( TC_slider::$instance , 'tc_slider_display' ), 0);
}