Se’ifim 11-13 and 15 raise other possibilities for exemption from tefillin, such as a scribe who is writing a mezuzah, tefillin, or a Torah scroll. Usually we say that if a fleeting mitzvah comes along, we undertake that mitzvah rather than the one we could come back to later. If the person has already started, though, he is an osek, is involved with a mitzvah, and need not stop.
Two significant caveats: that halachah was formulated when people did not take money for writing such parchments, did it purely for the mitzvah; while there are reasonable justifications for taking money, AH sees no reason to time one’s writing to the time for prayers.
Similarly, in theory, Mechilta Bo exempts one studying Torah from wearing tefillin (because Torah study accomplishes what the tefillin were supposed to). Nonetheless, especially when we wear tefillin so briefly, AH thinks the person should clearly take the time to wear the tefillin and then get back to study.
