Also, given imperfect correlation it is unclear how one should convert the scores. If I pick someone with SAT in top 1% I shouldn't expect IQ in the top 1% because of regression towards the mean.

The correlation is the slope of the regression line in coordinates normalised to unit standard deviations. Assuming (for mere convenience) a bivariate normal distribution, let F be the cumulative distribution function of the unit normal distribution, with inverse invF. If someone is at the 1-p level of the SAT distribution (in the example p=0.01) then the level to guess they are at in the IQ distribution (or anything else correlated with SAT) is q = F(c invF(p)). For p=0.01, here are a few illustrative values:

c   0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
q   0.5000 0.4080 0.3209 0.2426 0.1760 0.1224 0.0814 0.0517 0.0314 0.0181 0.0100

The standard deviation of the IQ value, conditional on the SAT value, is the unconditional standard deviation multiplied by c' = sqrt(1-c^2). The q values for 1 standard deviation above and below are therefore given by qlo = F(-c' + c invF(p)) and qhi = F(c' + c invF(p)).

qlo 0.1587 0.1098 0.0742 0.0493 0.0324 0.0212 0.0141 0.0096 0.0069 0.0057 0.0100
qhi 0.8413 0.7771 0.6966 0.6010 0.4944 0.3832 0.2757 0.1803 0.1036 0.0487 0.0100