Very odd that the girl is making it difficult for you to pay. My guess is that your concern is that she will spring out of nowhere and claim that she didn't get her money and then attempt to accelerate the note, demanding full payment.
Your summary leaves out one important detail which most notes include, which is where payment is to be made, for example to XYZ Bank, at a given address. The "little document" should indicate where and when to send the payment. If you have mailed all payments when due and the mail has come back, this would provide your defense to acceleration of the note. If you have the title you should have her address. Mail the checks there.
Without all of these details, my best advice is to keep track of your efforts to contact the girl and be prepared to pay her all of her past due payments. No attorney should ever provide advice based on a document without reading the entire document, and so this response is simply to give you a frame of reference.
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This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
Arguably, by the terms of the agreement that you posted (reproduced below), there is a notice provision where you must pay all past due payments within 30 days of notification by the seller before you are in default. As a practical matter, you should consider looking her up address on publicdata.com and sending the check to a physical address on her driver's license. You could also set up an escrow account and pay the funds into that so that the funds will be available and held in trust for her.
Acceleration of Debt upon Default
If the Borrower fails to make any payment when due for whatever reason and the Lender provides notice of such failure, the Borrower must effect payment of the amount due within 30 days, failing which the Lender can demand immediate payment of the entire outstanding Principal amount.
The lawyers above give good general advice, so I agree with them.
The keys to protecting you and your husband are in the details of your written agreement AND whether you can later show you took reasonable steps and measures to perform your duties under the contract. In order to protect yourself from a later lawsuit in Florida for an allegation of Breach of Contract, you should carefully document your performance (actions) so that you can later ( if you have to ) clearly demonstrate that you did NOT breach the contract. This will also protect you from any accelleration of the note or payments.
PRACTICAL TIPS: Here in Florida, most courts will rule that you tendered payment if you mail (certified mail, green card receipt) a personal check to the last known address of the seller. Your green card receipt will show the mail got there and who signed for it. Once the personal check clears your bank, you should be able to cheaply obtain a copy of the front and back of the check, which is pretty good evidence of who presented or cashed the check, and into what bank account it was deposited. If it is cashed for U.S. currency, it should include identifying info of the check, such as FL drivers' licensce number, or whatever ID the bank tellered checked to make sure the presenter was the person in the "Pay to the Order of" section of the check. If all these attempts to make payment fail - meaning it is still impossible to get her the money - you should take steps to make sure all the money due is segregated and available for her whenever she finally makes herself known. The above lawyer's reference to an ESCROW account is one example. One way to do this is to deposit the funds with an attorney, then notify seller through the above means that the funds you attempted to pay her are now waiting for her, held "in escrow" at a specific location, and giving her the instructions on how to collect the funds.
If you need help on this in the Gainesville, Florida area you can contact me and my firm.