Here are two simple tips you should be able to implement right away (if you're not already doing this):
https://dadario.com.br/preventing-docker-escaping-attacks/
> 1) Run the container as non-root user
> 2) [Use] a read-only file system
SELinux is probably your next step, which may be as simple as switching your host OS to RedHat/CentOS.
I'm not sure if you'll be able to use a VM on your current host, and using only one VM to host all your containers will not protect users from each other. (You could eventually use 1 VM for all free customers + VM per random batches of mid-tier paying customers + VM per premium customer.) VM escapes are much more rare than container escapes, and should be a solid line of defense separating your stuff from your users. The discussion I referenced recommended libvirt.
There is only one user, tux, which is uid 1002 and tux does not exist in the host's /etc/passwd.
The users do not have root access in the containers.
Cgroups is used to impose limits on RAM, number of processes, visible CPUs, etc.
I made this site in evenings and weekends, and have put it up for the public to use. I want find out sooner, rather than later, if the whole idea is flawed.