Interesting observation. Albert Barnes' Notes agrees with you (I added the underlining):
For by grace are ye saved - By mere favor. It is not by your Own merit; it is not because you have any claim. This is a favorite doctrine with Paul, as it is with all who love the Lord Jesus in sincerity; compare the notes at Rom_1:7; Rom_3:24, note.
Through faith - Grace bestowed through faith, or in connection with believing; see the notes at Rom_1:17; Rom_4:16, note.
And that not of yourselves - That is, salvation does not proceed from yourselves. The word rendered “that” - τοῦτο touto - is in the neuter gender, and the word “faith” - πίστις pistis - is in the feminine. The word “that,” therefore, does not refer particularly to faith, as being the gift of God, but to “the salvation by grace” of which he had been speaking. This is the interpretation of the passage which is the most obvious, and which is now generally conceded to be the true one; see Bloomfield. Many critics, however, as Doddridge, Beza, Piscator, and Chrysostom, maintain that the word “that” (τοῦτο touto) refers to “faith” (πίστις pistis); and Doddridge maintains that such a use is common in the New Testament. As a matter of grammar this opinion is certainly doubtful, if not untenable; but as a matter of theology it is a question of very little importance.
Whether this passage proves it or not, it is certainly true that faith is the gift of God. It exists in the mind only when the Holy Spirit produces it there, and is, in common with every other Christian excellence, to be traced to his agency on the heart. This opinion, however, does not militate at all with the doctrine that man himself “believes.” It is not God that “believes” for him, for that is impossible. It is his own mind that actually believes, or that exercises faith; see the notes at Rom_4:3. In the same manner “repentance” is to be traced to God. It is one of the fruits of the operation of the Holy Spirit on the soul. But the Holy Spirit does not “repent” for us. It is our “own mind” that repents; our own heart that feels; our own eyes that weep - and without this there can he no true repentance. No one can repent for another; and God neither can nor ought to repent for us. He has done no wrong, and if repentance is ever exercised, therefore, it must be exercised by our own minds. So of faith. God cannot believe for us. “We” must believe, or “we” shall be damned. Still this does not conflict at all with the opinion, that if we exercise faith, the inclination to do it is to be traced to the agency of God on the heart. I would not contend, therefore, about the grammatical construction of this passage, with respect to the point of the theology contained in it; still it accords better with the obvious grammatical construction, and with the design of the passage to understand the word “that” as referring not to “faith” only, but to “salvation by grace.” So Calvin understands it, and so it is understood by Storr, Locke, Clarke, Koppe, Grotius, and others.
It is the gift of God - Salvation by grace is his gift. It is not of merit; it is wholly by favor.
