Answer

Why shouldn’t the donor be able to decide where the donation goes? He is the one deciding to give, so obviously he can decide to whom. This is all the more so from the case of the benefit-right in terumah, which Jewish law rules is considered property—that is, the owner has the right to decide where the terumah will go, even though there he is obligated to give it. So if he is not obligated to give, it is obvious that he can decide to whom he will give it. It doesn’t seem to me that there is much to discuss here.
The question of the order of priority is a different question. After deciding that the owner is the one who decides, you ask according to what criteria he is supposed to decide. Here one must consider whether the order of priority in Horayot (see there 13a) applies here. On the face of it, yes (for why should this be any different from saving someone from drowning in a river, or from precedence regarding sustaining a person’s life), but I seem to recall that some halakhic decisors rejected this and said that in life-and-death cases this order of priority does not apply.
And in our case, where the person is not at all obligated to give his organs (as opposed to money, which you are obligated to give by virtue of “do not stand idly by your neighbor’s blood”), there is room for the reasoning that according to everyone there are no laws of priority here, and the entire decision is in his hands. He can always argue that if they obligate him to give to a woman or to a priest, he would prefer not to give at all—and that is his right. Therefore, it seems to me by simple reasoning that the decision is entirely his.