The SSCRA governs the rate the borrower can be charged on pre-service obligations during the period of military service. The contract between the servicer and the mortgage holder would dictate what the servicer must pay to the mortgage holder. Theoretically, the mortgage holder's contract should not give them a right to collect anything from the servicer that the servicer cannot collect from the borrower -- but it's a good reason to pull out the servicing contract documents to see precisely how they're worded.
Section 513, which you reference, provides protection to persons secondarily liable on an obligation. It is not designed to protect a lienholder. It provides, in pertinent part:
Sec. 513. Protection of persons secondarily liable
(1) Whenever pursuant to any of the provisions of this Act
(sections 501 to 593 of this Appendix) the enforcement of any
obligation or liability, the prosecution of any suit or proceeding,
the entry or enforcement of any order, writ, judgment, or decree,
or the performance of any other act, may be stayed, postponed, or
suspended, such stay, postponement, or suspension may, in the
discretion of the court, likewise be granted to sureties,
guarantors, endorsers, accommodation makers, and others, whether
primarily or secondarily subject to the obligation or liability,
the performance or enforcement of which is stayed, postponed, or
suspended.