Hello,
Did you ever figure out how to do this? I'm trying to update a shipping drop-down field in the Custom Forms section for the product through the API. It doesn't appear to be possible.
As nutty as this sounds, it looks like you can enable "Developer Mode" which then copies all your web pages to GitHub. The Custom Forms fields are in the webpage JSON file very clearly. I was thinking of then using the GitHub API to modify the JSON file which will then modify the Squarespace web pages accordingly. I would use Python or shell scripts on a local server to make the daily updates I need to do. Seems nutty, but should work. Squarespace API would be MUCH easier!
Thanks