How to rename ‘Tag Base’ with WPeC 3.8?

Tags are a custom taxonomy called product_tag in WPEC 3.8+, they’re not the same taxonomy as default WordPress tags so that’s why tagbase has no effect.

Line 315 in wpsc-core/wpsc-functions.php:

register_taxonomy( 'product_tag', 'wpsc-product', array(
    'hierarchical' => false,
    'labels' => $labels,
    'rewrite' => array(
        'slug' => "https://wordpress.stackexchange.com/" . sanitize_title_with_dashes( _x( 'tagged', 'slug, part of url', 'wpsc' ) ),
        'with_front' => false )
) );

*Edit- I somehow skipped over the part of your question where you point out the above, however, changing the slug in this file and then flushing your rewrite rules WILL change the slug, but you’re editing core files which is always bad.

The question I suppose should then be “Is it possible to override something set elsewhere in a register_taxonomy call?”