Apologies for the delay, but here's what my /etc/network/interfaces file looks like:
# Injected by Nova on instance boot
# This file describes the network interfaces available on your system
# and how to activate them. For more information, see interfaces(5).
# The loopback network interface
iface lo inet loopback
iface eth0 inet dhcp
hwaddress ether fa:16:3e:98:cf:35
The thing that I'm suspicious of are the IPs, as it's making me wonder if the issue might be to do with the fact that US-East-2 doesn't provide a private network by default, but I'm at a loss as to what to do about it, as with the interface configured as dhcp the IP addresses listed there shouldn't matter, so I'm not sure what else to change.
I had hoped to complete my migration tomorrow but it's looking increasingly like I won't be able to. From the sounds of it support staff have pretty limited access to instances which is frustrating, as I'm not sure why migration should even be my responsibility; I was forced to do all the grunt work to move to US-East-1 in the first place by the ridiculous two-week VPS root access ultimatum (despite the fact US-East-1 was a beta service which I would not have moved to if I'd had a choice), now I'm being forced to do all the grunt work to move onto US-East-2 because US-East-1 was apparently never fit for purpose judging by the massive outage a short time ago.
Edit: facepalms so it turns out the IP lines were the problem, as they should be omitted after setting to dhcp. Looks like it's another classic case of a terrible error message as "A start job is running for Raise network interfaces", doesn't exactly scream "you've left IP details in your dhcp settings". At least now my US-East-2 instance boots up normally, so the next challenge is to rsync across all the stuff that's changed since I first tried to migrate.