It looks to me as though a separate StyleInjector implementation could be provided that no longer batches style tag creation, but instead inserts each individually. When the app is compiled, the hash for each block of CSS could be computed (...minus any runtime value interpolation), and a generated file made available to the server so that appropriate CSP headers can be set on http responses.
Creating many individual css files and loading them via <link> tags is an option too, but won't load synchronously that way, unless you hit them all at startup (which then would mean that you may load them unnecessarily).
Alternatively, a nonce could be specified and injected with each style tag - but that seems like a weaker approach in general, since it requires making the nonce available to the page's script code.