Do CDN, such as Cloudflare, support SSE? The last time I looked, they didn't, but maybe things have changed.
No server traffic for 100+ sec officially results in a 524, so you could possibly make that keepalive interval longer, but I haven't tested it.
Make sure to have the new style cache rule with Bypass cache selected and absolutely make sure you are using HTTP/2 all the way to the origin.
The 6 connections per browser limit of HTTP/1.1 SSE was painful, and I am pretty sure auto negotiation breaks, often in unexpected ways with a HTTP/1.1 origin.
(it's not SSE in particular, but it demonstrates that you can have a long running stream like SSE)