If you're intentionally delaying that much, then your viewers are probably not going to interact with you. So they probably don't care that it's not actually live. Is there another reason why you can't do "live to tape" entirely, trim out the bad parts, and then upload or stream that?
One partial possibility to do exactly what you want, might be to have two parts to your rig:
- The "production" part records to MKV. It doesn't stream.
- The "streaming" part plays that same MKV, at the time that it's actually supposed to stream.
Effectively, you're using the recorded file as the really-long buffer that you want. The part that remains to be seen, is how to set a specific point in the file as you record it, and how to skip the player to that point. Unfortunately, I don't have an answer for that, except to have a dedicated person to manually note the recording timestamp and then manually skip the player to that timestamp. I don't know how to make just a button for each.
I think the file would have to be MKV to make that work, not MP4, because of the same mechanism that allows a crashed MKV recording to be played up to the crash point whereas a crashed MP4 recording is just gone entirely. You're practically using it in that failure mode, except that the "crash point" is steadily moving out as well, as the production side keeps writing to it.