(1) The question is whether the compositional account can do just to Chalcedonian Christology. But no Chalcedonian is committed to the claim that Jesus's human mind and human body would have composed a (complete) human being if they weren't assumed. Moreover, the inference from mind and body are components of a human person to mind and body (completely) compose a human person is illegitimate, even in the case of an ordinary human being, unless we have an account of mind-body union adequate to bridge the gap between the two. This is relevant to Chalcedon particularly in that the Councils when talking about minds are regularly concerned not with substantive components but with abilities: God assumes humanity and therefore human abilities. In other words, in Chalcedonian Christology God does not assume a human person, or even a potential human person; he assumes humanity and so becomes a human person with genuine human abilities (and the genuine organs of those abilities). The compositional account can allow for this unless we are assuming a very particular sort of account of mind-body union (namely, that mind and body are united as two substances are united).
(2) Morris's criticism of reduplication doesn't even make sense. Suppose the following is true:
(a) S is P (qua N)
(b) S is not-P (qua N*)
(c) P is univocal in (a) and (b)
These are not an inconsistent triad, because to create a contradiction it is not enough for P to be univocal; the predication of P must be univocal. But predicating P of S is different in (a) than in (b) -- that's precisely the point of the reduplication, that P, however univocal it may be in meaning, is not univocal in its predication. The triad is not enough to conclude simpliciter that 'S is P and not-P'. There are no logical problems with reduplication. The one and only problem is whether we can give an account of the Incarnation that allows us to reduplicate in this way. (The part of Senor's paper that argues that the compositional account fails to do this is the most interesting and important part of the paper; but I won't be looking at it in this post.)
(3) Contrary to what Senor seems to think, it is not any part of traditional theology to say that the divine persons are simple -- except insofar as the divine nature is simple. Therefore it does not contradict the doctrine of simplicity, as traditionally understood, if the Son is not simple in the Incarnation. (We know for a fact, in any case, that the Son is composite in the Incarnation because he has at least some parts, e.g., hands and feet.) Nor is it a problem for the Son to be material in the Incarnation. The only way materiality and composition would be a problem is if we said that God was material and complex in virtue of the divine nature. But, as Senor admits, the composition account doesn't imply this.
(4) Senor says:
So then we must ask, in virtue of what do the human body and mind come to be parts of GS, as opposed to mere instruments or some other kind of entities related externally and instrumentally to GS? If we think of an analogy with a non-divine person, I think we’ll see that there is no way for this compositional relationship to be established.
I think this is fairly clearly false; first, because an analogy is not an adequate argument for this sort of conclusion unless you show that the impossibility of the compositional relationship in the non-divine case is not due to an intrinsically non-divine feature. But more importantly, the claim is likely to turn out false in at least some cases with non-divine persons. Geordi LaForge's visor may be related externally and instrumentally to him, but his prosthetic eyes are not. It's not the fact of the prosthetic but the quality of its integration that is important; and the reason why people don't regard most of their prosthetics as parts of them is that their prosthetics are usually not well-integrated with them so as to be considered their own part (i.e., it's not possible for the part to be considered themselves in extension).
So I don't think Senor has given a very serious set of arguments against compositional accounts in general, although he has noted points that need to be considered in the formulation of such an account. In what I've said so far I haven't looked at his argument that the compositional account fails to yield reduplication in the proper way; this, I think, is the only part of the paper that really has a chance of working against compositional accounts. But I'll leave it for another post someday.