So, just to close this out: Writing directly to the emmc did not work. The system was unable to find the root file system. It had the wrong UUID somehow, so I changed it with tune2fs. Still no luck.
I then replaced the rk3399-pinebook-pro.dtb with the one that ships with Manjaro. That booted, but the laptop screen did not come on. I could only access it via the serial port.
Finally, I saw this post: https://forum.pine64.org/showthread.php?tid=17215
When I replaced rk3399-pinebook-pro.dtb with the version from Kali Linux, it booted, I got the display, and everything worked. I now finally have Armbian running from the emmc, albeit with the device tree blob from Kali Linux.