Figure out if we can optimize our GitHub actions with caching

[roypat]

In the past, our docker building GitHub actions used to benefit from some caching of action artifacts, which allowed the post-merge build of the docker container to be skipped in favor or just reusing the artifacts from the pre-merge build (at least I remember something like this happening). It seems like a few months ago this stopped, but it'd be nice to get this functionality back, if only to avoid docker-container-building turning into a whole-day activity.