In the meantime, it's not like you can migrate your Signal, Telegram, iMessage, or even Gmail/Hotmail accounts. I think Matrix needs a few more client/server implementations before the spec can't truly be set in stone.
MSISDN (phone number) identifiers landed on the backend this afternoon; implementation in the Riot clients will be coming very shortly.
There are broadly two ways of solving it:
1. have a naive implementation where users can configure their accounts to replicate between sets of servers, and clients have primary and fallback servers they can talk to if the primary isn't available.
2. switch to a p2p model where each device has its own server, and so account data is automatically replicated across multiple devices. This has a host of other advantages too (e.g. you can own your data without running your own server; you can adopt metadata-protecting federation transports; you can still use all the existing apps today as the client-server API remains the same; you can still bridge with the Matrix network of today).
#2 is obviously way more work, and is effectively rewriting the federation side of Matrix. However, Matrix is designed to evolve and we're not ruling this out from happening at some point. Meanwhile #1 is more likely to land in the nearer future. We haven't got it scheduled in yet, but it's very much on our minds!