Hmmm. 
I think I see where you’re going with this. Let me have another go…
@ganncamp - I think we may have some success… 
Based on Bronze Badge A being awarded through the post wrench or by giving a reason on the /admin/users/{user_id}/{username}/badges page:
Then I think this is indeed possible. 
WITH badge_count AS (
SELECT
user_id,
granted_at,
post_id,
ROW_NUMBER() OVER (PARTITION BY user_id ORDER BY granted_at DESC) AS row
FROM user_badges
WHERE badge_id = 110
AND post_id IS NOT NULL
)
SELECT user_id, granted_at, post_id
FROM badge_count
WHERE row % 5 = 0
AND (:backfill OR post_id IN (:post_ids))
(Adding in the AND post_id IS NOT NULL protects it from if someone is awarded one without a reason, otherwise it breaks)
I have just tried it out and fast-forwarded by triggering the GrantBadge background job and my test user has finally received the full credit they deserve.
I then awarded them 5 more Badge A for 5 more different posts and ran it again: 
