Persisted Cash Dues Invoice: Remove / cancel single line on zero-balance invoice

What is the supported way to remove or cancel a single line for one contact on a fully paid, zero-balance persisted cash dues invoice? My workflow is set up to use ProcessCashAdjustment, which is working well for cashes with a non-zero Balance. However, a no-op when the Balance is zero have me wondering if I should be supporting that, and how.

PUT /api/Subscription/~{partyID}|{productCode} with CancelledAsOf set would work, and it is scoped to the one contact, and I think it will cascade to the invoice line because the invoice is IsLinkedToSubscriptions. Is that a supported approach for this case, or would it bypass logic that ProcessCashAdjustment would normally apply?