It took some experimentation, but I got your approach to work. I didn’t realize until I dug a bit that I had to enable the snippet in settings even after it was loaded (easy fix), and I discovered I was adding the css class to the wrong note (the embedded note, when it needed to be the note it was embedded in). The Webpage HTML plugin still inserts a bunch of space below the embed, but it’s not nearly as apparent without the block quote formatting. I also discovered it inserts white space at the bottom of any published note.
tl;dr It’s not perfect, but I got it to work pretty well and learned some Obsidian CSS in the process.