TR, I'm not sure I agree with your "within 15 days" analysis. Unless I'm misunderstanding what you are trying to day.
From 1024.21
Time of notice. (i) Except as provided in paragraph (d)(2)(ii) of this section:
(A) The transferor servicer shall deliver the Notice of Transfer to the borrower not less than 15 days before the effective date of the transfer of the servicing of the mortgage servicing loan;
(B) The transferee servicer shall deliver the Notice of Transfer to the borrower not more than 15 days after the effective date of the transfer; and
(C) The transferor and transferee servicers may combine their notices into one notice, which shall be delivered to the borrower not less than 15 days before the effective date of the transfer of the servicing of the mortgage servicing loan.
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The opinions expressed are mine and they are not to be taken as legal advice.