So the Codemasters forums have now been changed to read-only, and instructions have been sent out to EU players via email on what to do next.
This involves checking this transfer website until it spits out some concrete information on how to sort out a US account/ transfer. (Link updated: thanks mbp.) Apparently this may not be active for another 2/3 days. So long fellow hobbits, see you on the other side.
Welcome to Spinksville! 
Huzzah!
Can’t help but thinking communication on the important aspects of this transfer have been a little bit “off” but if it all goes well, I guess we won’t have a problem :p
Looks like the migration page is now functional, but has been difficult to access owing to load. Just managed to complete the migration at 2:00am and currently doing a UI update. EU servers are still down though. Good luck everyone.
Oddly enough that lotro-migration website is frozen in time and doesn’t actually link to anywhere else.
When I updated the client it sent me to here instead: https://transfer.lotro.com/
That link actually allows you to log in and start the process. I didn’t manage to complete the transfer though because it keeps giving me errors.
I had the same problem, which is why I eventually did it at 2 A.M. I presume they can’t cope with the load.