Audio broadcasting in the background (on the locked screen of iOS, Android), is there an analogue of Icecast2?

Question

Audio broadcast

Good day! Tell me, please, there is a need for audio broadcasting for mobile devices.
Mandatory conditions - minimum delay (no more than 5 seconds), not strong out of sync (synchronism is even more important than delay), work in the background (playback continues even if the smartphone is blocked).

So that if several people turn on at the same time in the room, then there is no such thing that one is in a hurry for 5 seconds, the other is 4 seconds behind, the third is already 20 seconds ahead. That is, the thread should keep track of the buffer and skip if a lag is noticed.

I managed to set up Icecast2 with a delay of 3 seconds, more or less suitable, but what if there is some better solution?
I tested Nimble Streamerwith the SLDP protocol - an amazing solution, it fits all the criteria, if not for one but. Everything is great on android, but for bitten apples again everything is in one place, it doesn’t play on the iPhone at all, you need to install the SLDP Player application, with which it still falls silent when the screen is locked.
And so they are great, I would even pay them for some Pro if it solved the problem. This is an awesome product.

Thus, I see no alternatives to the less than ideal Icecast2. I tried to get an icecast stream with Nimble Streamer - the delay is wild, Icecast2 KH with its 3 seconds is better. I tried it on YouTube, normally, about the same 3 seconds, but YouTube wants money for listening to it on the locked screen. And not from me, but from each of the listeners.

In principle, Icecast2 would suit me, but if one of the listeners has a playback twitch for a second (you never know, the Internet is bad), his stream will lag behind forever until the page is refreshed.