I'm not sure how you'd run a double-blind experiment on this. You can single-blind the experimenters, but the participants are always going to know whether they've been drilling IQ tests.
Your point about counterfactuals is good, but… subjectively, I ended up with a better understanding of IQ test genre conventions (which is also why I bang on so much about "culturally-specific": they really are). My speed at solving the problems doubled or tripled, and my accuracy went from 80%-ish to near 100%. This did not translate to any improvements to my real-life skill at anything (although, I suppose it might've generalised a bit to other multiple-choice exams). I've got a lot more evidence to analyse than just an n=1 scatter plot.
> the participants are always going to know whether they've been drilling IQ tests.
I'm not asking you to actually do this, but the participants (and experimenters!) don't necessarily have to know what you're testing. Maybe get one to drill IQ tests, one to drill Latin, one to drill chess and one to drill the piano.
Does your ability extend to IQ tests with other patterns? Also, does it extend to logic puzzles?
No, it actually slows me down on IQ tests that don't follow the genre conventions. (I used to approach them with a fresh mind – and I can still do that, if I have time to get into that mindset, but it's not always my default.) But I almost never see those, so…
It doesn't extend to logic puzzles, which I've always been quite bad at. (I find the Professor Layton games hard enough to be actively unfun, despite their beauty.) I can solve problems if they're contextualised, but my approach for solving logic puzzles is "identify a general algorithm, then execute it", which is quite slow.
As I've been telling you: IQ is extremely artificial; and doesn't measure general intelligence, because there's no such thing as "general intelligence". The "g factor" is a statistical regularity, but any statistician can tell you that while all sustained statistical regularities have explanations, they don't necessarily correspond to real things.
The problem with "I've gone through this" is it's hard to analyze the counterfactual.