It turns out a combination of the two ideas can be used. After delving into the accounts-ui package, it turns out that it contains only one .less file. The actual template is included in accounts-ui-unstyled, which is automatically included when accounts-ui is added to a meteor project.
Hence, the CSS can be removed as follows:
meteor remove accounts-ui
meteor add accounts-ui-unstyled
You are then left with the raw HTML, which can be styled as you choose.