The largest number of people have applied this year

It seems a number-transparent use of number can, in fact, take the when separated from it by some other word:

ii If [the same / expected number of people] come next time we’ll bring in professional caterers.

iii [Only the tiniest / stated number of people] have done a better job than that.

iv [The other / record number of mistakes she had made] were easily corrected.

v [The average / required / perfect number of people] have applied this year.

So, the ban on the for the number transparent use seems intended for the case in which the is the only pre-head element in the NP, where there's nothing separating the from number. Of course, it would be possible to write:

If [the number of people expected] come next time, we'll bring in professional caterers.

Only [the number of people stated] have done a better job than that.

[The number of people required] have applied this year.

Thus it seems that as long as number is modified so that we can pick out a particular number, number-transparent number can take the.

[The largest number of people] have applied this year.

I suspect the superlative largest is queering the deal here.

Last year's 50,000 applicants was well above average. However, the largest number of people ever [have/has] applied this year.

To my ear, either have or has is possible, but I prefer has, probably because of the was in the first sentence. This is a matter of notional agreement working with a different sense of number than CGEL's transparent sense.

All of last year's 50,000 applicants were drug tested. However, the largest number of people ever [have/has] applied this year, causing this policy to be reviewed.

Notional agreement may be more acceptable here due to the parallel structure.

In terms of transparency, the superlative or comparative has to match the sense of what it is being compared to. I score that as non-transparent with respect to the PP.