I have had good experiences with the free NGINX RTMP Module¹ for basically doing the same thing. I just have a cheap US and EU cloud instance. Stream OBS in multiple qualities to the US endpoint and have it auto pushed to the EU endpoint. Using this module, both endpoints use RTMPS and generate HLS and DASH. Then added a little HLS.js² player and can easily serve a small private viewing party, at multiple stream qualities with auto quality/bandwidth adjustment.
¹ https://github.com/arut/nginx-rtmp-module
² https://hls-js.netlify.app/demo