If you’re gunna use an adapter anyway then it makes it irrelevant whether or not there’s a headphone jack in the phone. People in this thread talk about how you can’t use expensive wired headphones with your mobile devices anymore as if adapters don’t exist.
I think the problem is less timing the messages, and more that the messages from earth will just get redshifted more and more as the ship accelerates, which will require an ever larger antenna to pick up. This also has the affect of bandwidth tending towards 0.
You cannot transmit information through entangled particles, so probably not.
Looks like you best get to switching.