With Mux you can enable "Redundant Streams" (multiple CDN's used in HLS manifest) which I think solves the issue here. We are also a big Mux customer but admittedly haven't made the full switch to redundant streams, although our testing was very promising. Since their ingest is all GCP I don't think that was affected by this, and it would have just been delivery.
https://www.mux.com/blog/survive-cdn-failures-with-redundant...