Since I have very little expertise in these areas, I was just wondering if anyone knew about efforts to estimate the impact of these confounders and adjust for them.

One way to assess the confounders' impact is to estimate heritability using a method that doesn't rely on making assumptions about adoptees or twins, and see whether it gives higher/lower results. Here's a paper that did so to estimate height's heritability in a sample of 3,375 sibling pairs:

• Peter M. Visscher et al, 2006. "Assumption-Free Estimation of Heritability from Genome-Wide Identity-by-Descent Sharing between Full Siblings", PLoS Genetics, 2(3), e41.

I'd personally delete the first two words from that paper's title, but it nonetheless avoided whatever issues there might be with using adoptees & twins, getting a heritability estimate of 80% (with a 95% confidence interval of 46% to 85%), broadly comparable to those from older twin studies.