Another update: I've been stoooopid. MyFonts does provide a CSS version of the license code along with the @font-face rule, I just didn't spot it. It's the .css file in the main folder of your font Kit. (The text in the StartHere.html document that I copied and pasted into my initial post in this thread is just a sample text with a sample webfont build ID, not your personal one!) For Squarespace all you need is the code in the .css file.
Customer support sent me this link with detailed instructions. (The article is a bit old, you can ignore the @import rule bit since MyFonts no longer use tracking scripts and it doesn't appear in your font Kit.)
https://blog.edross.co.uk/post/77473634153/using-custom-fonts-on-squarespace-with-myfonts