Ok, spent a little more time, got a variety package of auto body sandpaper, and was mindful of the "don't ruin it in the quest for perfection" advice. Turns out that point became obvious - I could tell that I wasn't improving it anymore, so I did a final block sanding up to 600 grit and tested it out. Shuddering is now barely noticeable and I'm sure it will improve over time by itself. Calling it a day. Thanks again to all.