Drupal FAPI: How do I change a value in the validation function?

In the following code, I am trying to update the underlying form to a new value, but the value does not seem to update properly.

function msul_tgif_xml_basic_search_form_validate($form, &$form_state) {

  //$Offset is computed properly as verified by dpm.

  $form_state['complete form']['SearchOptions']['Offset']['#value'] = $Offset;
}

function msul_tgif_xml_basic_search_form_submit($form, &$form_state) {
  $form_state['rebuild'] = TRUE;
}

When I return to msul_tgif_xml_basic_search_form, $formstate['values']['Offset'] properly shows the new computed value, but when I recreate the form with the new value, it does not update properly. The relevant portion of the msul_tgif_xml_basic_search_form function is:

      $form['SearchOptions']['Offset'] => [
                    '#type' => 'textfield',
                    '#title' => t('Start with result:'),
                    '#required' => FALSE,
                    '#default_value' => 
                         isset($form_state['values']['Offset']) ?
                         $form_state['values']['Offset'] : 1,
                    '#size' => 6,
                    '#description' => t('blah'),
                    '#element_validate' => [
                              'element_validate_integer_positive'
                    ],
              ];

As I said, the regenerated form still contains whatever the user typed in last and does not update according to what the code is telling it. Any ideas of what I am doing wrong...I have spent about 25 hours trying to get this to work.

I have tried the above, I have also tried form_set_value().

I don't feel this is the right answer, it seems like a kludge but it does work, I changed the value of $form_state['input']['Offset'] and that worked. Hopefully this helps someone else as well.