I came across your post a couple hours ago as I was struggling with the same issues.
I now have a working custom theme using a Mustache template for the login page.
Here's what I discovered :
- I had to override render_login() in my theme's theme/mytheme/classes/core_renderer.php to add whatever template variables I needed to the template context
- I somehow only had to use theme/mytheme/templates/core/login.mustache
I hope this helps.