Getting down to brass tacks, we are assuming a lot when we compare IQ numbers from different tests.

You keep on saying "assuming" and Vaniver keeps on telling you that there is no need for assumptions: we have data. It's not hard to give the same people different tests and then look at how do the scores correlate.

In fact, that's how the whole concept of IQ came into being -- IQ is an estimate of the general intelligence component (g) that is common to performance on a variety of intelligence-measuring tests.