How do I alter a form submission handler?
Stupid question but have you cleared cache to register the new hook?
Also, try inspecting the form in hook_form_alter to make sure you are attaching the handler to the correct action.
Lastly, I've found that I usually need to reorder the array to include my handler first in order for my actions to actually trigger on form submissions using Drupal core forms that have existing handlers.
As an example, I did like:
$form['actions']['submit']['#submit'] = array_reverse($form['actions']['submit']['#submit']);

which will reverse the array. I also sometimes use array_unshift to pop my handler at the start of the array if the other handlers need to retain their order.