Don't underestimate the bandwidth of a transport fleet of data disks.

Seriously, don't: most bulk-archiving is done by shipping drives even today, with only incremental backups being done via network transfers.
Once we've made the handover of the one-time pads, we can transmit the actual communications over the extranet, with mathematically-provable impossible to hack encryption. The actual communication will be as instant as the extranet allows, and given that we are a very rich corporation we can get fast access to the extranet fairly easily. Now, this isn't a long-term solution, certainly; we'll need a full-duplex network between our research labs at least, which means that the number of one-time pads we'll need will go up quadratically as the number of lab sites we have, but by the time that becomes anything like an issue we will have the QEC tech as part of our Cabira research and it won't be an issue.