You are exactly right about Luther and exactly right that Canon 9 specifically rejects justification by faith alone (sola fide) and not justification by faith (which is what Rome holds).
The disagreement is not over whether works have any place in the Christian faith, but it is over the place of works strictly in the matter of justification. Rome teaches that good works are necessary to justification, with the caveat that those works which are necessary to justification are worked in them by Christ, as a fruit of grace (as you said). Protestantism teaches that a man is justified by faith alone, apart from any works, but solely resting on Christ’s work accomplished for us (Phil 3:9; Titus 3:5). Rome teaches justification by infusion of righteousness; Protestantism teaches justification by imputation of Christ’s righteousness (Rom. 4:5, 8). For Rome, justification is a process; for Protestants, an instantaneous event.
Protestants understand faith as a mere instrument, as an open hand receiving Christ’s righteousness; Rome conceives of faith as a meritorious work affording a person a title to justification (faith formed by love).
We both agree that saving faith is never alone but will always work. Where we disagree is in seeing good works as the fruit of justification vs. seeing good works as necessary causes to justification. Faith produces good works of man, but faith itself is not a good work of man.
As Luther said, “[Faith] is a work of God, not of man, as Paul teaches (Eph. 2:8). The other works He works through us and with our help, but this one He works in us and without our help.” -The Babylonian Captivity of the Church
In the end, if the gospel is to remain good news, justification must be grounded solely on what Christ has done for us, and not on anything He does in us (Phil. 3:8-9). Here is the disagreement. What Rome teaches is actually a form of the Galatian heresy, wherein we begin by grace and finish with works (again, in the matter of justification), rather than the Christian gospel, which is all of grace and all of Christ.