We all know situations when you cannot go open source and freely distribute software - and I am in one of these situations.
I have an app that consists of a number o
Sounds like Docker is not the right tool, because it was never intended to be used as a full-blown sandbox (at least based on what I've been reading). Why aren't you using a more full-blown VirtualBox approach? At least then you're able to lock up the virtual machine behind logins (as much as a physical installation on someone else's computer can be locked up) and run it isolated, encrypted filesystems and the whole nine yards.
You can either go lightweight and open, or fat and closed. I don't know that there's a "lightweight and closed" option.