As a more general solution, there's a CloudBees plugin for Jenkins to build inside a Docker container. You can select an image to use from a Docker registry or define a Dockerfile to build and use.
It'll mount the workspace into the container as a volume (with appropriate user), set it as your working directory, do whatever commands you request (inside the container). You can also use the docker-workflow plugin (if you prefer code over UI) to do this, with the image.inside() {} command.
Basically all of this, baked into your CI/CD server and then some.