Synchronization may be an issue. Compressing analog will be an issue. That won't be something that's handled just by antenna switching, that's going to take something to unpack the audio. This is where digital shines.
Again, if this was a viable solution, it would have been developed. While I can certainly appreciate the desire to make it work just for the challenge, there are probably very good reasons it wasn't done in the past. Remember, hams are usually a resourceful bunch and a lot of development has happened in the hobby. Maybe not so much anymore, but it does still happen. Your particular challenge isn't anything new, not on the ham side, not on the LMR side.
You say you want to do this with existing radios, but I don't see a way to do that without some heavy modifications.
I can certainly understand the desire to come up with a unique solution that hasn't been tried before. That's what the hobby is about. But I think you may not be fully understanding the challenges of making this work. If you can make it work, it's not going to be easy or cheap, and it's going to take more than just antenna switching.