Re: 3 - if you read the full paper you'll see that on its own a work sample test has (barely) the highest predictive value (but a lower confidence in that than GMA which is more heavily studied). This quote I think does more to demonstrate that GMA and integrity are less correlated than GMA and work product testing or structured interviews, which is intuitive.

Re: 4 - I'm not sure why you would consider a take home test less valid as a work sample test and then prefer a whiteboard test. Certainly the latter is less representative of real working conditions. (I probably would not want to work in a place where whiteboarding is more representative, at least!)

Your other two points are reasonable threats to validity but I don't think especially strong ones. The research covers many different professions so I think the onus would be on you to explain why software engineering is so different.