Teach Me How To Pack UV Islands via Command Line on Windows or Ubuntu

I need to be introduced to a method for packing UV islands for high-poly models via command line. I have models that are >3 million faces that have a LOT of empty space between islands and I'd like to optimize this space and spit out a smaller texture that holds the same size islands (no scaling them down) but is a smaller overall file (e.g. the original is 8192x8192, the output would be 6000x6000 with all of the space between the islands removed). I can run this on any number of CPU cores, but it needs to finish within 60 minutes every time. This also needs to be triggered via command line and run without a GUI loading. I'm certain this must exist, but I haven't been able to find it anywhere. Find it for me, show me how to use it, and I'll pay you. To prove that you can do this, I have attached a model with a texture to this project. Download it, pack the islands, then re-upload it to prove that you can do it - and let me know the total cost for the software you used. Once I've selected you for the project, we'll talk about how you used the software you did via command line, then we'll consider the project complete once I can reproduce your process on my local machine. My budget for software is small, so free/cheap solutions are definitely better than expensive ones. I look forward to your methods, however hacky they may be! I use a Windows Server 2012 R2 instance, so whatever software you're using has to work on that operating system. If you have something that runs on Ubuntu 14.04, that'll work too - but you will need to help me set it up to ensure it is working, as I'm not as familiar with the environment and setting up dependencies.