If the inbuilt SSS nodes don’t get you to where you need to be, you could try full volumetric SSS instead.
I created a node group a while back. Just be aware that it’'ll likely be slower than the SSS node (plus you’ll need to play with the number of volumetric bounces in the render panel).
Thanks! That did seem to help somewhat. I modified the radius, and also applied the scale, which I forgot to do. These two things seemed to do the trick.