This is directly from the borrower agreement I received when taking out my loan here. (I'm still waiting for it to be issued but I'm a long term investor here as well and see no reason for it to not complete)
"Prepayments and Partial Payments. Borrower may make any payment early, in whole or in part, without penalty or premium at any time. Any partial prepayment is to be applied against the principal amount outstanding and does not postpone the due date of any subsequent monthly installments, unless Lender otherwise agrees in writing. If Borrower prepays this Note in part, Borrower agrees to continue to make regularly scheduled payments until all amounts due under this Note are paid.
Lender may accept late payments or partial payments, even though marked "paid in full", without losing any rights under this Note."
Based on what I bolded from the borrower agreement, there is no liability to LC to cash a check marked "Paid In Full" that obligated them to treat the note as fully settled. I believe they are just notating that the check was marked as such and would continue any standard payment methods or collections methods as needed on the account. One of the note links I had clicked on and reviewed indicated that there were collection efforts after the notation on the payment. Had I seen this thread earlier, I would have offered to purchase those notes from you

Edit: Actually this was from the Loan Agreement, not borrower agreement.