"Wish: make a SD card image that, when inserted in the SDcard slot, causes a bootable Armbian OS image to be written to eMMC from that SDcard, followed by boot from eMMC."
Forgive me if I'm missing something in the question, but it seems like this is an available option, it always works for me to end up with "boot from eMMC & system on eMMC" following the Armbian Getting Started instructions.
Burn the image to SD, insert SD and power on, it boots quickly and you then get IP address and set user/PW while still on SD, then start the install script with "armbian-install" and choose the option to have boot / OS both on eMMC. I'm using 32GB eMMC and have had success with 32GBSD card, though I purchased a few 16GB Sandisk Ultra A1 ($6 each) which are safer for this as they are smaller than the eMMC
When the armbian-install script is done (and you chose the correct option for eMMC as shown below), shutdown and remove SD card, then you are all set to boot from + run OS from just that eMMC
/ John