There are shortcuts for selecting the first and the last layer.
Alt + . → Top layer
Alt + , → Bottom layer
Photoshop default keyboard shortcuts
There's also a shortcut for selecting the next layer above and below: Alt + [ and Alt + ].
Additionally, there are ways to select layers from the document, which I'm a big fan of. Just point at a layer in the ...
For this exact scenario you can press Alt+] — that is a shortcut for Select Next Layer but if you have the top layer selected it'll jump back to the first one. The same is true for opposite: Alt+[ will select top layer if you have the first selected.
Sorry for my english I'm from Costa Rica. But It's easy you just have to put your background image out of any artboard (like a background layer) and when you export your files in the export option, just clik "include overlaping areas".
There's likely a faster way to do this somehow (and if I had to do this for more than a handful of frames I would have probably used ffmpeg) but the fastest way I was able to do this in GIMP was by first, preparing the overlay as a layer, selecting and copying that layer, selecting the bottom layer in the layers tab, pressing Ctrl-V to paste the overlay, ...