Everything you say is contradictory.
I think it is more likely that I have been misunderstood.
You say that the Son can’t have anything different from the Spirit
Where did I say that? The Son differs from the Spirit in His hypostatic property of being Begotten, just as the Father differs from both as being Unoriginate and being cause. The Son and the Spirit cannot differ by nature (that is, they cannot differ in what they receive from and share with the Father), as this would render one a creature, but they do differ according to their particular mode of existence (τρόπος ὑπάρξεως), which is what distinguishes their hypostases. That is what St. John of Damascus taught in the quote I provided from Orthodox Faith.
but in the case of the Father, he can, for only he can beget the Son and only he can be source of the Spirit.
See above, the Father alone is cause because this is a distinguishing mark of his hypostasis. If being cause were a property of nature, then either the Spirit should share in it, or the Spirit should be a creature.
If the Spirit can proceed from the Father, the Spirit can proceed from the Son.
This is not true, because if the Spirit proceeds from the Father and the Son, it means that the Son participates in a hypostatic mark of the Father, or causality is a natural property of the Godhead. To take causality and apply it to two persons of the Godhead instead of either three or only one would make it neither an hypostatic property, nor a natural property, but an accident as in things composed and created.
You can’t have it both ways.
Nor do I want it both ways. You have constructed a straw man.
The Father does not have attributes not possessed by the the other Persons of the Trinity.
Sure He does. This was self-evident enough that Duns Scotus used this very fact to defend the formal distinction, for if, as Scotus argued, paternity were not formally distinct from that which is communicable, the Son would also be Father, and possess paternity. Then there are the Eastern Fathers too, who universally understand that the Father, Son, and Holy Spirit differ in their hypostatic properties, their particular modes of existence, those being being Unbegotten, being Begotten, and Proceeding
The other two Persons are not inferior in any way.
Untrue, for the Son himself in John 14:28 said, “the Father is greater than I,” and both St. Basil the Great and St. John of Damascus understand this passage in reference to causality, for the Father is greater than the Son with respect to being the cause of the Son. By nature, however, the persons are identical, and none is inferior.
The Role of Father in generating the Son is not an attribute, but instead signifies a relationship. This is also true of the roles of both the Father and the Son in breathing forth the Spirit. It signifies a relationship, not a special attribute.
This reduces the three hypostases of the Trinity into being mere prosopa, distinguished not by a particular property or mode of existence (that is, being robbed of their ontological content), but only by subsistent relationships.
You are wrong in supposing that if the Son has the power of spiration the Spirit must also have it, because spiration is not a power
But you yourself have referred to Spiration as act, and all acts have an associated power (dynamis or potentiality) and actuality (energeia). If spiration cannot be conceived of as a power the neither is it an act.
nor does any Person of the Trinity have a power that the other Persons do not have.
That is again because you conflate hypostasis with nature. No person has any natural power that another does not have, but according to hypostasis, the Father has causality, which neither the Son nor the Spirit have, as taught by Gregory the Theologian in his 34th Oration, when he writes: “All that the Father has belongs likewise to the Son, except Causality; and all that is the Son’s belongs also to the Spirit, except His Sonship…”
Spiration signifies relationship, and that relationship is the love between the Father and the Son.
So then do you deny that Begetting and Spiration are acts?