I'm pretty sure that you could include this in the install.sh script in the build_image directory (see https://blog.martdj.nl/2021/12/06/domino-docker-explained-part-6-creating-your-own-customisations/). That way, you could create your own custom image with Nomad web server, so you don't lose it if you remove the container.
One the one hand, I'd love to describe how to do it, but I know that by the time I'm done, Daniel will have included it in his domino-container script as a simple parameter which will do all the work, so it feels a bit pointless.