So do 538 and The Economist try to take these polls, back out their biases, and reapply different ones? Or, to borrow a phrase from Trump, "unskew" them?
No, these models weight the polls by quality (variously judged), they don't reweight by voter. This weighted average of polls is then used, along with factors like time until the election and economic conditions, to give a probability distribution over election outcomes (which no poll can give you, no matter how you weight it).
"Unskewing" polls dates back to 2012 (Dean Chambers and UnskewedPolls.com). He was doing what you describe - applying his own likely voter model to all polls, based on party affiliation. It did not work. Better to use each pollster's likely voter model as it is, since then you have an ensemble and possible cancelation of error.
