Layered Navigation Not Showing on Every Category in Magento 1.9

In addition to changing the URL which is being rendered, you'll need to rewrite Mage_Catalog_Model_Layer_Filter_Attribute::apply():

/**
 * Apply attribute option filter to product collection
 *
 * @param   Zend_Controller_Request_Abstract $request
 * @param   Varien_Object $filterBlock
 * @return  Mage_Catalog_Model_Layer_Filter_Attribute
 */
public function apply(Zend_Controller_Request_Abstract $request, $filterBlock)
{
    $filter = $request->getParam($this->_requestVar);
    if (is_array($filter)) {
        return $this;
    }
    $text = $this->_getOptionText($filter);
    if ($filter && strlen($text)) {
        $this->_getResource()->applyFilterToCollection($this, $filter);
        $this->getLayer()->getState()->addFilter($this->_createItem($text, $filter));
        $this->_items = array();
    }
    return $this;
}

$this->_getResource()->applyFilterToCollection($this, $filter) is where the ID is passed in. Your change needs to map the option text to the ID prior to this. Something along the lines of the following will get you going:

public function apply(Zend_Controller_Request_Abstract $request, $filterBlock)
{
    $filter = $request->getParam($this->_requestVar);
    if (is_array($filter)) {
        return $this;
    }
    $filter = $this->getAttributeModel()->getSource()->getOptionId($filter);
    $text = $this->_getOptionText($filter);
    if ($filter && strlen($text)) {
        $this->_getResource()->applyFilterToCollection($this, $filter);
        $this->getLayer()->getState()->addFilter($this->_createItem($text, $filter));
        $this->_items = array();
    }
    return $this;
}

I'm a bit concerned as to what effect this will have on caching, etc. but at least this will head you down the road to a solution.

I am not sure how your homepage is configured, but by default you can't make it happen.

Try adding a Category block on your homepage, by adding

{{block type="catalog/product_list" category_id="8" template="catalog/product/list.phtml"}}

on you Homepage CMS's page content. Replace category_id with your category's id.

Cheers.