FYI: Some of the stuff you described above is done in phusion/baseimage (based on the official Ubuntu image), e.g. providing a proper init(-like) system incl. cron etc. You might want to check this out.
Without having analyzed the Docker file in detail, I suppose many of the “powerful” features you need can be done by copying a script into the image and executing it on every docker run, doing some checks if bootstrapping is needed and just going ahead and run the app if everything is set up. This will incure a cost on every launch of the container but that should not happen too often.
The bootstrap process would detect if the container has not been set up yet (i.e. default / missing config files) and immediately shutdown the container in that case. The “proper” config can then be loaded into the container via volumes or a custom, user-generated Dockerfile (based on the discourse image) so deployments are easier and do not require packaging and shipping a full image.
Some of the preliminary checks (like for system ressources) can still be performed within the launcher script (or moved to the bootstrap process within the container, I don’t see a problem with that) – disk size checks are IMHO unnecessary (at least before launching the container) since docker would complain if there is not enough disk space to download the image itself. But I would move most of the other checks into the container and have the launcher script be a simple entry point for beginners or lazies (like myself).