Shirah and masaos at shnayim mikra (and Ta'am Elyon/Tachton)

We know that one is supposed to use the טעם העליון is supposed to be used during the עשרת הדברות only during a public reading, when, to some extent, we reenact the event in shul. When reading the עשרת הדברות privately, (such as when reading them to fulfill the מצוה of שנים מקרא ואחד תרגום,) the טעם התחתון is used, since when learning the פסוקים one is supposed to read them with the trop that breaks them down gramatically (and musically) the normal way one would break down a פסוק. Does it then follow that the שירה and מסעות (and the ''על צבא'' phrases in פרשת בהעלתך) one should privately read them with the regular trop, since the the tune used to read them elides over much of the trop? I assume that the פסוקים traditionally read on a high key can still be read that way privately since the trop remains the same.

Melech