I'm currently in the process of switching from YouTube to Piped and was getting fed up with rewriting YouTube links myself. I finally found an extension that can do this with a relatively easy setup:
I dont have this problem. But maybe your instance or browser is causing problems? Kavin.rocks was causing problems for me in LibreTube, but this was fixed after switching to piped.yt.
There's a few of them that seem to work fairly reliably, but the rest just don't play or have error messages on load. Take a bit of time to keep hitting the ping instances button and add the ones that seem to respond well to your list.
With the way youtube throttles these connections, it's not going to be the same experience, but I'm stubborn like that.