While I did have some success with in-place install shenanigans, I eventually settled on creating a customised install ISO for the distribution I wanted (with a script to have it automatically listening for remote shell connections, and so on), using isohybrid on the ISO (which makes the ISO's first sector also a bootable MBR), and then simply dd if=install.iso of=/dev/sda - right over the top of the partition table and everything.
It's inelegant, to say the very least, but it works just fine! I'm pretty sure I saw that technique used a few times during Twitch Installs Arch Linux, during the more exotic segments when some joker hijacked the effort temporarily by installing Windows 95, and TempleOS, and so on.