I was successful in booting the prebuilt petalinux image from the "old Zybo" this morning.
Here are my steps. I'm not sure if they are "minimal" in the sense they may have unnecessary portions, but they did work for me.
1) Create a petalinux project from the provided .bsp given here using the 2017.4 version of the tools. This is downloaded from:
https://github.com/Digilent/Petalinux-Zybo/releases/tag/v2017.4-1
2) Partition my 32 GB sd card with two partitions. You can do this from either Windows or Linux, but I personally did this from Windows using the disk partition tool. The first partition is about 1 GB for the "boot" stuff, and the second partition is for "data" that I want to give the operating system outside of the petalinux project. Both are formatted with Fat32 with the default block size. You can add support for other file systems using petalinux -c kernel, but Fat32 is the default in the given .bsp.
3) Copy the "BOOT.bin", "image.ub" from the prebuilt image folder inside the petalinux project onto the "boot" partition of the SD card.
4) Eject the SD card. Insert into the Zybo board.
5) Swap the boot jumper pins to "SD". Plug in the UART USB cable.
6) Turn on the Zybo's power.
7) Launch a serial monitor such as Putty with 115200 baud, 8 data bits, 1 stop bits, no parity, no flow control.
8) The Zybo board boots and logs the user in as root.
Hope this helps.