Teffilin and Teffila are two separate Mitzvos. We wear Teffilin while davening because Teffilah needs a Guf Nukkei and ao does Teffilin. Sow we “kill two birds with one stone”. However, if someone does not have Teffilin available and it comes time to daven, I woulds aay he should daven without Teffilin and put Teffilin on later in the day. And if someone missed Shachris, he still has the mitzva of Teffilin. The mitzva of Teffilin is the entire day whereas Shachris is only in the morning.
That being said, I don’t see why you should have to put your Teffilin back on to repeat Shemonei Esrai.
SiDi™