kesivas sefer torah - is one yotzei b'shutfus?

I heard in a shiur that the campaigns to collect donations for writing a letter/pasuk in a sefer torah are not a kiyum of kesivas sefer torah because the person donating does not personally own the sefer being written, which is a basic criteria of the mitzvah. The Rambam writes that the mitzvah is to write a 'sefer torah l'atzmo', which the person giving the shiur compared to all other mitzvos sheb'gufo like hanachas tefillin. The last point strikes me a wrong because one can appoint a shliach for the kesiva. However, the first point is a significant objection. At the time I argued that one indeed does own the sefer being written - all those who contribute form a shutfus of joint ownership. Does one need exclusive personal ownership to fulfill the mitzvah? This issue is debated by the Minchas Chinuch and the Ohr Sameiach at length. One objection raised focuses on the toeles of the mitzvah, which is to create a sefer that can be learned from. The Rosh takes this so far as to write that in our times the mitzvah of kesivas sefer torah is fulfilled through the purchase of seforim. The moment one party of the shutfus takes the sefer to learn, does that not render it inaccessible to all the other parties to learn from and negate the mitzvah? My thinking was that the potential for any party to have access is sufficient, but the point can be debated. A textual proof: in Sanhedrin 21a Rava says one is not yotzei kesivas s"t by inheriting a sefer - the mitzvah is kisvu lachem, writing it for yourself. Abaye quotes a braysa that derives from 'v'kasav lo' that specifically a king 'lo yisna'eh b'shel acheirim', cannot be yotzei with a sefer written for someone else - the implication being that an ordinary person would be yotzei with such a sefer written for someone else. The gemara answers that the braysa's halacha is referring to the unique second sefer torah that must be carried by a king; Rava's din refers to the sefer everyone is obligated to write. Achronim ask: if one is yotzei kesivas s"t b'shutfus, why did the gemara not answer Abaye's question by saying the braysa's din of 'v'kasav lo' excludes a king from sharing with 'acheirim' in the form of shutfus because no one else can use royal property; however, an ordinary person is yotzei b'shutfus and is only excluded based on Rava's din from being yotzei b'yerusha? I'll give you some time to think it over...