It makes sense what you are saying, I suppose I am getting hung up on the other aspects of “assent”. I think we will all agree that saving faith is a faith that works, no matter what our doctrinal distinctives may be.
Intellectual assent does not need to have anything to do with belief, really. I assent to a number of scientific and mathematical facts and postulants that are not at all related to belief systems. Does intellectual assent mean agreement or acknowledgment? That seems to be more cognitive in origin. Then there is the matter of the will. When it comes to faith, as you say, it is a “verb” in that I choose to place my faith in Christ by an act of the will. This is why it seems so similar to “believe”. Jesus calls us to “believe” in Him, does He not?
However, I do agree that the CC does shy away from “faith alone”, maybe not so much because of how these terms are used, but because of all the additional trappings that are attached to the “solas”. It may be one area of doctrine that we share more than we realize.