@luke I eventually got this to work. When I ran git lfs push --all origin master, git was asking for my password for my netlify git endpoint. So I tried upgrading netlify-cli and the lm plugin as per your comment here:
yarn global upgrade netlify-cli
netlify plugins:install netlify-lm-plugin
netlify lm:install
netlify logout
netlify login
Then it was still asking for my password. So I had to edit .git/config to add these lines:
[credential "https://<MY_SITE_ID>.netlify.com"]
helper = netlify
[credential "https://<MY_SITE_ID>.netlify.app"]
helper = netlify
Then after a final git lfs push --all origin master, my large files showed up and are served through the /static folder.