I dont think the problem is intractable at all. We have the internet now and can just test people. We don't.
Yes, that would be less accurate than a test administered in office by a professional, but it would also be more accurate than basing it on educational attainment or standardized tests intended for other purposes.
With a little effort the tests true purposes could easily be disguised. These very clever researchers know this, they just won't.
I don't know what to tell you about reducing this problem to an online survey and hoping for the best. There are people doing actual science --- including with modern IQ tests --- working on these problems. I think the bigger thing here is that, outside of message boards and Twitter, there just aren't that many people interested in a global country-by-country inventory of "average IQ".