Warning: This could break and completely mess up your categories and tags. I’m only promising this worked for me on my install for now (who knows, maybe I updated things wrong and huge problems will occur a month from now). Use caution. I take no responsibility.

 
# create tags for every category
INSERT INTO wp_term_taxonomy (term_id, taxonomy)
    SELECT term_id, "post_tag"
    FROM wp_term_taxonomy
    WHERE taxonomy = 'category';
 
# copy category-post relationships to tag-post relationships
INSERT INTO wp_term_relationships (object_id, term_taxonomy_id) 
    SELECT 
        object_id, 
        (SELECT i.term_taxonomy_id
         FROM wp_term_taxonomy i
         WHERE
             taxonomy = 'post_tag' AND 
             i.term_id = wp_term_taxonomy.term_id)
    FROM wp_term_relationships 
    JOIN wp_term_taxonomy ON 
        wp_term_relationships.term_taxonomy_id = wp_term_taxonomy.term_taxonomy_id 
    WHERE taxonomy = 'category';
 
# update tag count cache
UPDATE wp_term_taxonomy 
    SET count = (SELECT count(*)
        FROM wp_term_relationships
        WHERE wp_term_relationships.term_taxonomy_id = wp_term_taxonomy.term_taxonomy_id);
 
# remove all categories and category-post relationships
DELETE FROM wp_term_taxonomy WHERE taxonomy = 'category';
DELETE FROM wp_term_relationships 
    WHERE term_taxonomy_id NOT IN (SELECT term_taxonomy_id FROM wp_term_taxonomy);

The INSERT INTO ... SELECT was a fun little query to write with its subselect. After running this, I just had to create and apply categories to my posts (I’m going with Biz, Code, Games, and Life for now) and update my templates.