Even with the calligraphy pen's mass set to 100 I get these issues. But increasing it a little certainly helps matters. I've just had a bit more discussion on Reddit and it does seem like there is no perfect solution and that may just be the nature of Inkscape. I'll play around with mass a bit more.

I posted my question to the Inkscape subreddit after deciding I'd probably forget to check back here regularly, but I never found a solution on there. I'll just link you directly to the post since some discussion took place there: https://www.reddit.com/r/Inkscape/comments/92gvy4/help_why_are_my_lin...