Not only do I agree with Bradd on the implications of your opinion, FastJack (and the need to have it spelled out, if so), but, When you say "two-thirds of the SR4A and FAQ all treat Specialization as an addition to the dice", I have to disagree from a RAW perspective.
The only place that treats it as an increase to your
skill vice an addition to your
dice pool is the FAQ, which, not being an errata is a collection of opinions and interpretations, and doesn't trump the book.
In the book itself, you have two places which talk about how to add in specialization. One of them specifically calls it a dice pool modifier, the other says the following:
Specializations add 2 dice to any tests made for that skill when the specialization is applicable to the test.
Not only does that not say it adds to the skill, it says it adds to the
test which sounds like an informal way of saying
dice pool to me. That would make it a dice pool modifier, as page 68 explicitly tells us it is.
Barring an errata, the only option available in the RAW is to treat it as a dice pool modifier.
You're proposition of making a third category, skill modifiers not subject to the limitations of max augmented skill, seems cumbersome compared to treating it as a dice pool modifier, and unnecessary, to boot.