I'm not sure the invidious: protocol supports live streams, it seems like it's only fetching a single fragment from the HLS stream. What you're trying works for me using a direct invidious instance URL, e.g. https://inv.nadeko.net/watch?v=cmkAbDUEoyA.
Anyways, the idea is to mimic the ytsearch1: feature but for invidious -- search for a video id based on its title, drop id on an invidious stance, and play it. I've got half of it.