OK, success!
I added an entry to my /etc/fstab and rebooted:
none /tmp tmpfs noexec,nosuid,size=25%,mode=0755 0 0
And now when I run df I get:
$ df -h
Filesystem Size Used Avail Use% Mounted on
udev 7.8G 0 7.8G 0% /dev
tmpfs 3.9G 9.7M 3.9G 1% /run
/dev/sda1 432G 246G 168G 60% /
tmpfs 7.8G 135M 7.7G 2% /dev/shm
tmpfs 5.0M 4.0K 5.0M 1% /run/lock
tmpfs 7.8G 0 7.8G 0% /sys/fs/cgroup
none 3.9G 4.0K 3.9G 1% /tmp
...
/dev/sda1 432G 246G 168G 60% /mnt/btrfs-ssd
/dev/sda1 432G 246G 168G 60% /home
tmpfs 1.6G 80K 1.6G 1% /run/user/1000
Interestingly, it lists /tmp as none type. But, anyway, I’ve now run the snap command again, and voilà, I have a pi3.img file. I haven’t checked if it actually works yet, but that wasn’t the problem.
I do also have a bug open on Launchpad, I’d actually opened that before asking this question, but it wasn’t getting much love.
Why should ubuntu-image care how the /tmp directory is mounted? Perhaps the mode=0755 line? If so though, especially since it’s run as sudo, it should surely be able to figure it out?