So I mounted the old system root and bind mounted all of the right system paths ( /dev, /sys, /proc, /tmp, /run, /var/run ) into it and chroot in, I’m able to just run minecraft under the old openjdk-8 in the Ubuntu 18.04 filesystem. Yay! Oh, I also had to copy /etc/resolv.conf into the chroot so it could resolve hostnames, and had a little trouble getting pulseaudio to work instead of forking its own instance with no output sinks until I realized that when I ran su - psusi to switch to my normal user inside the chroot, it cleared the XDG_RUNTIME_DIR environment variable which was needed to point pulseaudio to the existing server socket.
Also I’m really liking this Sway window manager.