In the end the changes we made were as follows:
1) we used the food processor to mash up the pumpkin (oh yeah, we used pumpkin instead of butternut squash) to get some air in there
2) we cut our gnocchi into smaller pieces.
3) my boyfriend experimented with a new dough-making method that involved adding flour to the paste while it was on the cutting board instead of in a bowl, but in my opinion this just made a bigger mess.
These don't seem like major changes, but for whatever reason this time our gnocchi were much better on the first day. We also served them in The Best Sauce Ever, so really they could have had the consistency of cardboard and still been delicious.
Pumpkin gnocchi with a pumpkin butter sauce (pumpkin butter, salted butter, salt, pepper, cream, pecorino cheese), topped with chopped apple & crumbled vegetable chips
Panko-crusted and fried barely-ripe tomatoes with grated pecorino