I will refer to the point herrison raised in his post regarding the interpretation of the ing clause in the original sentence:
My original purpose was to write an undergraduate text on digital
communication, but experience teaching this material over a number of
years convinced me that I could not write an honest exposition of
principles, including both what is possible and what is not possible,
without losing most undergraduates.
This is what herrison said in his post:
Some modifiers come before what they modify (for example, single-word
adjectives usually precede the modified nominal), but many kinds of
multi-word modifiers are regularly placed at the end rather than the
beginning of a phrase in English.
This is key for understanding the ing clause function in the original sentence. The clause "teaching this material over a number of years" is way too heavy to be pre-modifying the noun referent. This reflects the general constraint placed on noun modification in English - noun pre-modifiers cannot (normally) be post-modified (or complemented) themselves. The authors of CGEL recognize a verb phrase as a form intermediate between a verb and clause. So, verb phrases can pre-modify noun, but clauses (normally) cannot. In this example, the noun phrase headed by "experience" and modified by an -ing clause is equivalent to "teaching experience". The ing clause modifier is pushed behind the noun it modifies simply because it is too heavy. Other than that, the phrase can basically be reduced to "teaching experience". It is what we are talking about here.
This is important to notice because a noun and an -ing verb can stand in a quite different relation from this. So, if we rephrased the sentence a bit we could say like:
My original purpose was to write an undergraduate text on digital
communication, but with teaching experience approaching ten years now,
I am convinced that I could not write an honest exposition of
principles, including both what is possible and what is not possible,
without losing most undergraduates.
The ing clause "approaching ten years" modifies the noun "experience" in a different way from the participial clause in the original sentence. The grammar is quite different and so is the interpretation. This -ing clause is not parallel to what would be the pre-modifying counterpart - "approaching experience". This use of ing clauses is similar to that of relative clauses. The natural position of this clause is after the noun antecedent.
Or, to use another possible rephrasing of the sentence:
My original purpose was to write an undergraduate text on digital
communication, but I gave up the idea, years of experience teaching me that I could not
write an honest exposition of principles, including both what is
possible and what is not possible, without losing most undergraduates
.
This is yet another different relation between the head noun and the ing verb. The phrase "(years of )experience" is interpreted as the subject of the following verb "teaching". Unlike the previous two participial clauses, this one is not understood as a dependent within an NP. The whole thing "years of experience teaching me that.." is loosely attached to the rest of the sentence structure.