Fortunately, I stumbled upon one possible solution.  The method doesn’t involve creating a full-blown module, rather, just a few database modifications using phpMyAdmin.

Summarized, the process comes down to:

1. Create a new row in the eav_attribute table, one that mimics a category’s meta-description attribute with everything being the same except for a unique identifier and a label.
2. Create a new row in the eav_entity_attribute table, to provide a sort order for your newly created attribute, following in the format footsteps of the existing rows.

For the fully detailed procedure, see Create Custom Category Attributes with phpMyAdmin

With Text attributes such as Name and Description, you can do something like:

$product->setName( 'My Sweet Shirt' );
$product->setDescription( 'This shirt will make you look good, thus impressing girls.' );

Unfortunately, this won’t work for attributes whose values are predefined.  Instead of cursing Magento, think of it as a data-integrity/validation measure.

Anyway, assuming you already have a $product object, our overall process will be to:

1. Load an attribute object for the attribute you want to work on
2. Load the collection of that attribute’s values
3. Make your choices (different for Dropdown and Multiselect)
4. Save the product

1. Load an attribute object for the attribute you want to work on

$attribute = Mage::getModel('eav/entity_attribute');
$attribute->loadByCode( 4, 'color' );

2. Load the collection of that attribute’s values

$values = array();
$valuesCollection = Mage::getResourceModel('eav/entity_attribute_option_collection')
	->setAttributeFilter( $attribute->getId() )
	->setStoreFilter( Mage_Core_Model_App::ADMIN_STORE_ID, false)
	->load();
 
foreach ($valuesCollection as $item) {
	$values[$item->getValue()] = $item->getId();
}

3. Make your choice – DROPDOWN

$product->setColor( $values['Blue'] ); // just do whatever you need to code 'Blue' instead of hard-coding it

3. Make your choices – MULTISELECT

$product->addData( array(
	'color' => $values['Blue'] .','. $values['Red'] .','. $values['Black']  // just putting together a comma-separated list of values
) );

4. Save the product

$product->save();

This builds off the solution posted by member “icvu” here: http://www.magentocommerce.com/boards/main.php/viewthread/69925/ — specifically the addData() part.

Thanks, and have fun setting attribute values.