"Docker is not an acceptable security solution for this, since it's most certainly possible to break out of containers."

Could you point to some resources that show that it is possible to break out of Docker containers? I understand that there have been bugs in the past that have caused this (using that to conclude that glot.io shouldn't use Docker is a bit like saying OpenSSL is now useless because of heartbleed) but it seems unlikely that breaking out of containers is possible due to the way Docker is designed.