My main strategy with drawing faces in the past was "play by ear", and indeed, when I look at the art I made during that period I now notice a lot of wonkiness. The Loomis method was honestly an eye-opener for me, in the sense that it finally gave me a simple set of rules to follow when drawing heads/faces to achieve consistent results. While I'm still far from being good at it (I, like OP, struggle a lot with eye position), I feel like I've improved compared to the wonky face era.
If you're interested, Youtuber Jazza has a short book about drawing faces that you can buy from his website. It covers the basics and gives tips on how to convey specific looks and character types. I would recommend it if your art is on the more cartoony side - if like me you prefer a more realistic look, then Jazza's faces can get a little too exaggerated and over the top.