We use WebSockets in the bot that we work on and we had a similar issue with certain VPS providers. I may have missed/glossed over everything you have tried, but, folks were losing their connections with our bot between 5 - 15 minutes out depending upon how busy chat was. The fix was we to provide an option to send the PING to Twitch more often. It turned out that some VPS providers, like Azure, were shutting down WebSocket connections within 3 minutes if not kept alive. I am not saying this is your issue, but it was something that killed us only with WebSockets.
Cheers