You asked for a Debian version, there is a Linux version which should work on Debian. I'm sorry you have to go through extra steps to get a working runtime environment, but that's kind of how the cookie crumbles when you're using Linux.
At the moment that's probably the best I can do for you. Getting a version that doesn't depend on the .NET runtime would probably involve rewriting the whole thing in a language that isn't C#, and considering I have made a grand total of $6 ever on Dreambox that's probably not super feasible for me. I also don't have access to Chromebook hardware, and do not plan on obtaining one, so a native app is also probably off the table.