1) Verbal abilities are probably more relevant to educational attainment than other specific abilities, but g is by far the most relevant. It would be odd if the error only affected verbal ability but not measured g.
Incidentally, the LBC study –– if memory serves –– gave the children two separate IQ tests, one of these the 1937 Stanford-Binet, and Ritchie et al. also controlled for SES in their study of educational effects. Two full-scale IQ tests (though with a strong verbal bias) plus an SES measure jointly compose an immensely reliable composite measure of IQ. Still confounded by differential rates of maturation, of course.
2) Of course those are valid criticisms! But, as Sandra Scarr said of twin studies, the holes don't go straight through. Logically invalid appeal to authority here –– I doubt that any decent intelligence researcher today believes in zero or zero-ish effects of schooling on IQ (you excepted), although they might consider those effects hollow.
I don't want to sound condescending, but you really should read Ceci's 1991 paper on education and IQ.
What a priori reason is there to believe that schooling does not affect IQ? I can think of a few: zero shared environment on adult IQ, but substantial shared environment on total educational attainment; the lack of effects of compensatory education; the lack of effect of school quality on achievement, as measured by Coleman. Good arguments, to be sure. But I do not think they outweigh those I've listed above.
With respect to shared environment, suppose that educational differences in affluent countries account for 10% of total variance in IQ scores (probably too high) and that total years of education exhibit shared environmentality of 20%. Then the total amount of IQ variance that could be explained by education-related shared environment is 2%. (Add to this quality of nutrition and other factors, and you could get more. So 2% is conservative, by my argument. Maybe 5%?) You would probably know better than I whether behavior genetic knowledge can, at the present time, reliably distinguish a 2%/5% from a 0% shared environmental effect. I suspect so, in which case the education-affecting-IQ theory faces a real problem. As you know, though, when behavior genetic studies include families living in genuine poverty, there are inconsistent effects –– sometimes, but not always, the shared environmentality goes up.
A final argument: IQ tests contain obviously scholastic information, vocabulary, arithmetic problems, and so on. How likely is it that education does NOT affect these? We have good evidence, if I am not mistaken, that there is some shared environment effect on educational achievement scores.
3) Kindly post the Danish study. If that replicates, it would suggest adult educational gains to be hollow, perhaps limited to crystallized intelligence or verbal ability (as found by Ritchie et al.).
Suppose that gains do end up generalizing across tests, as with the Flynn effect. Could they still be hollow? Yes, if there are some sources of variance common to all tests but not shared by real-world criteria.
Motivation is one. The relatively rigid and sequential format of "test reasoning", relative to the messier and ambiguous forms of real-world reasoning, are another. (This distinction was drawn by Ulric Neisser, and used by Sternberg in his triachic theory.)
More research! More research!