Kesivas sefer torah b'shutfus (II) and challah

The mitzva of writing a sefer torah is derived from the pasuk 'kisvu lachem es hashira hazos'. We raised the issue whether the plural 'lachem' in the pasuk can include a sefer jointly owned and written by a partnership, a shutfus. Rava (Sanhedrin 21b) darshens 'kisvu lachem' to teach that a sefer torah must be written for oneself - one is not yotzei by yarshening or buying a sefer written for someone else. Abaye challenged Rava from a braysa which darshens 'v'kasav lo' in the parsha of melech to teach that a king must use a sefer written exclusively for himself - the implication is that everyone else can be yotzei with a sefer written for others. The gemara resolved the issue by saying both halachos are true - Rava's derasha applies to a regular sefer, but we need the braysa's derashsa for to teach us the halacha for the second sefer a melech is obligatedd to write. If writing a sefer b'shutfus is acceptable, why could the gemara not answer that the extra limud by a king comes to exclude shutfus?
Appropos of parshas hashavua, the Ohr Sameiach uses an analogy to challah to address this proof. Dough jointly owned by a yisrael and aku"m is patur from hafrashas challah - the aku"m is not just personally exempt from the mitzvah, but his ownership causes even the portion of dough owned by the yisrael to be exempt. If a king were a shutaf with a yisrael is writing a sefer, the yisrael could not make use of the sefer to learn from because a king's property cannot be used by a hedyot. Since the yisrael fails to fulfill his obligation of writing a sefer with this shutfus (because the entire toeles of the mitzvah is to have a sefer one can use for learning), even without the pasuk of 'v'kasav lo' it is understood that the king is not yotzei b'shutfus, just like a yisrael cannot be obligated in challah if half his dough is owned by someone who has no kiyum mitzva of challah.
Is this analogy to challah convincing? A yisrael is a bar chiyuva in the miztva of kesivas sefer torah, but is precluded from using the sefer for a side reason having to do with hilchos melachim; an aku"m is not a bar chiyuva in challah. I need to mull this one over...