In the Reformed tradition, the teaching of Isaiah chapter 11 IS taught, but because the seven gifts listed apply to the Messiah, a distinction is seen between that passage, and the gifts of the Spirit that Christians may receive, as in Rom. ch. 12, 1 Cor. ch. 12 and Eph. ch. 4. Care needs to be taken not to so inflate a Christian with ideas about the fruit of the indwelling Spirit's gifts that he or she begins to think prophecy that applies to Christ should also apply to them. Your helpful quotes from the Catholic perspective on Isaiah ch. 11 show that this passage is being applied to individual [Catholic?] believers (no doubt having first acknowledged application to Christ).
Examples of Reformed care are shown here, in two Reformed writings. I cannot date the first book as I only have the 27th edition of the original. The writer of the Introduction (Dr. R.A. Torrey) had come across the original 20 years earlier, but there is no date for either.
"Isaiah XI The peaceable kingdom of the Branch out of the root of Jesse, vss. 1-9. Vs. 1, And there shall. The prophet having described the destruction of the Assyrian army under that of a mighty forest, here takes occasion to represent the GREAT PERSON, who makes the subject of this chapter, as a slender twig... Vs. 2, the Spirit of... [lists many related scripture texts, but none that speak of Christians having gifts of the Spirit] Vs. 3, shall make him [and through to vs. 9, speaks only of 'Him' being the object of these gifts of the Spirit.] The Treasury of Scripture Knowledge from Canne, Browne, Blayney, Scott & others; pp. 436-7. Bagster London, Revell New Jersey (Capitals the author's.)
Of note, it goes on to link striking the earth with "the rod of his mouth" (vs. 4) with Revelation 1:16, 2:16 & 19:15 where the risen Christ is individually identified with this action: "...and out of his mouth went a sharp two-edged sword ...with it he should smite the nations". Again, no related scripture references point to Christians.
Another point that is found in the Reformed tradition is speaking of spiritual gifts that may appear in individuals who yet lack the grace of God - which never could be said of Christ! Consider:
"Still farther may an individual go in an approximation to the evidences of true godliness, and yet remain unregenerate. He may possess eminent spiritual gifts - fluency of expression in prayer - great exhortatory powers - eloquence in preaching - clear discrimination in spiritual subjects - the discerning of spirits - the gift of speaking and of interpreting of tongues; yet continue a graceless soul, retaining the 'carnal mind' and the 'heart of stone.' What, we ask, is the most instructive and solemn page in the history of the Corinthian church? - that which teaches us that great gifts may exist in union with great impiety; in other words, that gifts are not graces, that an individual, or a community of individuals, may possess the gifts that edify, and at the same time be destitute of the grace that humbles and sanctifies." The Work of the Holy Spirit, p.40, Octavius Winslow, 1961 reprint. The original was published in 1891 with the title, Personal Declension and Revival of Religion in the Soul. (Emphases the author's.)
My answer avoids all reference to modern views about spiritual gifts, such as in Pentecostal, Charismatic and Alpha Course circles. But in the Reformed tradition, I would suggest that the difference between that view of Isaiah ch. 11 vss 1-9 and the Catholic view is mainly due to keeping a clear distinction between the role of the Holy Spirit in Christ as the individual, the Messiah, "full of grace and truth" (John 1:14) and the fruit of the Holy Spirit's gifts in believers in Christ. There may be much more to it than that, of course.
As to your question about moving away from St. Augustine's stance on this point, I would just quote your statement, "Between the 11th and 13th centuries medieval theologians explored the connection between the Holy spirit gifts and the virtues until the theology of the gifts and virtues were settled with St. Thomas Aquinas's theology." Therein lies the answer. The Reformed tradition found much in Augustine's writings with which to agree, but by the 11th century they found much medieval theology with which to disagree. It also goes without saying that just because one finds much to agree with in Augustine, is not to say that one will therefore agree with everything! Nor must all the links and interpretations of later scholars of necessity be bound to follow.
My answer would end with the words of Christ on this matter. In Luke ch. 4, Christ read from another portion of Isaiah (ch. 61), saying at the end of his synagogue reading, "This day this scripture is fulfilled in your ears". Isaiah, as we know contains many prophecies about Messiah, all of which were fulfilled in Christ. His relationship with the Holy Spirit is unique, as all Isaiah's prophecies about Messiah show. Reformed Christians may be keen to avoid applying to themselves what uniquely applies to Christ, as that would be presumptuous.