Registrant and Contribution status remains "Partially Paid" even though amount owed was paid off
I think this may be resolved in 4.7 based on what I read in JIRA (there's a variety of tickets on payments topic so it's hard to tell whether one of them will solve this per se but it seems so). I'll test 4.7 and will come back to this topic if it's not solved. For now, I'll mark this as the answer.