Dear Rabbi Kornfeld,
Rashi says in two places that when the Gemara says that a person blew one long Tekia, he meant it for the last of Malchios and the first of Zichronos. How could a person have such a long hefsek between the "pshuta lifoneha" and the Truah (i.e. long enough to daven Zichronos?) Or did Rashi have a different seder of tekios than we have?
Sharp question. It seems that Rashi is relying on the Halachah of Rebbi Yochanan (beginning of 34b), who says that if one blew the nine Teki'os through the entire day (with a long Hefsek between each blast), he is Yotzei, for their is no problem of Hefsek with the Teki'os.
Thus, in the case as Rashi describes it, one blew one long Teki'ah with intention that it serve as the last Teki'ah of the set for Malchiyos and the first Teki'ah for the set of Zichronos, and then the person stopped blowing in order to Daven Zichronos, and then he continued blowing the Teki'os of Zichronos, starting with the Shevarim-Teru'ah of Zichronos.
Let us know if you come up with any other approach.