You could write a script that just restarts your container, make sure unprivileged users cannot edit it, and do one of two things:
- make a sudoers entry for your unprivileged account to call just that script as a user in the docker group with sudo
- use setuid on the script to have it execute from the docker group even when executed by users
Are you running them from your user session? If so, when you log out it will stop your processes, unless you have enabled ‘linger’ mode.