Faceit correction and/or weight painting advice

I’m trying to use the FaceIt plugin in 2.9 to created shape keys, but I’m a newb and finding that my results are fairly horrifying. Here’s an example.
The landmarks Placement:


And the result when I attempt a wink.

I suspect that the problem is that they eyes are just too big and I’m pushing the plugin past its limits. Anyone have any advice? It it just a matter of weight painting to try to get a smoother behavior of the eyelids, or is it possible that I’ve misaligned the landmarks in a way that I’m not seeing?