Maybe I forgot to mention, but the dpkg index would live inside the overlay as well. The idea is to make a chroot environment with the benefit of not having to duplicate anything that's already on eMMC. I also mentioned that probably one overlay per SD card would be needed.Not intentionally, no. If you just use an overlay filesystem and regular dpkg to install stuff you may wind up with a situation like this quite easily though.
Install package P1 with dependency D with sd card S1 as the write overlay, insert SD card S2, install package P2 with the same dependency D, dpkg sees D as installed and doesn't install it on S2, remove S1, now you have P2 but no D.
dpkg would only see what's on one overlay when the user (or some script) chroots to into it. And then when a package is installed it will forcibly land in the same overlay.