> you would just load up the your Alcubierre station wagon with a bunch of backup tapes

Tapes have mass. Unless we learn to suppress inertia, it would be easier to encase the message photons in an Alcubièrre field.

Not suppressing inertia is indeed a problem, unless the message the kind you intend to be understood primarily by virtue of its infinitely inverse ratio of complexity to fidelity.

The secret to time travel is to drive backwards.

The secret to time travel is to forget that you're moving forwards with time, so you'll float instead. Many people have paid other people to surprise them into forgetting that they're moving forwards in time, so they'll float instead.