Best way to customize styles of embedded comments?

I need to customize the styles of the embedded comments to fix some margin/padding and color issues.

I've tried appending new styles to the head inside the iframe but unsurprisingly I'm getting cors errors.

Is there a template somewhere I can edit that controls the markup and styled of the embedded comments iframe?

Or should I follow the advanced embedding instructions and pass a custom function that adds the styles to the child iframe like this:

Vanilla.embed.fn.functionName = function(args,...) { … }

Those instructions seem to be more for embedding the forum instead of just embedding the comments so I'm not sure if they are applicable in this scenario.