Create and add attribute group with attributes to all attribute sets

It's a lot easier to do it via setup script. Here is an example:

// Add new Attribute group
$groupName = 'My Attr Group';
$entityTypeId = $installer->getEntityTypeId('catalog_product');
$attributeSetId = $installer->getDefaultAttributeSetId($entityTypeId);
$installer->addAttributeGroup($entityTypeId, $attributeSetId, $groupName, 100);
$attributeGroupId = $installer->getAttributeGroupId($entityTypeId, $attributeSetId, $groupName);

// Add existing attribute to group
$attributeId = $installer->getAttributeId($entityTypeId, ATTRIBUTE_CODE);
$installer->addAttributeToGroup($entityTypeId, $attributeSetId, $attributeGroupId, $attributeId, null);

Note: $installer variable is instance of Mage_Eav_Model_Entity_Setup class. You can look there for further reference. You can also look in app/code/core/Mage/Catalog/sql/catalog_setup folder for some more examples.

Using an installer script

Try

$filters = array(
    'my_attribute_id_1',
    'my_attribute_id_2'
     ..
);

$product_tab = 'General';

foreach($filters as $value){
    $eavModel    = Mage::getModel('eav/entity_setup','core_setup');
    $attributeId = $eavModel->getAttributeId('catalog_product', $value);

    foreach($eavModel->getAllAttributeSetIds('catalog_product') as $id) {
        $attributeGroupId = $eavModel->getAttributeGroupId('catalog_product', $id, $product_tab);
        $eavModel->addAttributeToSet('catalog_product', $id, $attributeGroupId, $attributeId);
    }
}