It seems as if going first in Vintage is a big advantage despite the fact that going second gives you an extra card. So what if the choice was play or draw 2 cards? How would this change impact Vintage? (There are several variations to this. For example, you could have the draw2 occur before mulligans.)
I wouldn't hesitate to draw two every time, because it would give me the equivalent of an Ancestral Recall, right off the bat.