Link State to Country in Custom Fields
Well, after hunting around on my own, I think I may be able to answer my own question.  For others who want to "link" a Profile's custom field Country to a custom field State so that changing the country automatically refreshes the list of States, I was able to do this via the civicrm_buildForm hook.  This hook allows one to modify attributes of specific form elements, and that's all I needed to do.

As of 4.5, I think, the Country/State chaining interaction is done through data-callback and data-target attributes, not through a JS snippet. So, one way to make this work is to add those specific "data-" attributes to the custom fields via the hook.

Here is my example code (apologies for bad formatting).  My State field is custom_99 and my Country field is custom_122.  Once I applied the attributes, my team registration form finally worked as before; changing the Country updates the State list.

function xxx_civicrm_buildForm( $formName, &amp;$form )
{
  if ( $formName == 'CRM_Event_Form_Registration_Register' ) {
    // Modify the classes/attributes for country and state fields so the country dropdown will dynamically update the state dropdown
    $form-&gt;updateElementAttr('custom_99', array('class' =&gt; 'crm-select2 crm-chain-select-target crm-form-select', 'data-callback' =&gt; 'civicrm/ajax/jqState', 'data-name' =&gt; 'custom_99', 'data-select-prompt' =&gt; '- select -', 'data-empty-prompt' =&gt; 'Choose country first', 'data-none-prompt' =&gt; '- N/A -'));
    $form-&gt;updateElementAttr('custom_122', array('class' =&gt; 'crm-select2 crm-chain-select-control crm-form-select', 'data-target="custom_99"', 'placeholder' =&gt; '- select -'));
...
} // end function


By the way, civicrm_buildForm is a pretty powerful hook, I use it to set defaults and required fields based on the Event Type and values of other custom fields.