Jan -
Forgive the stupid question, but are you changing the port settings to what YOUR computer says? I just keep reading what you are posting and wondering if you are checking your own settings. Once it is set for your own com port you should not need to change. And it sounds like it is communicating when you do that.
If you were using Inkscape and Signcut I would tell you to be sure you are setting your origin button as not setting that will cause the mat to spit out - and would assume you do that with MTC too but don't want to steer you wrong with that part.
Keep sharing - we will help you figure it out. I just don't want to further complicate things for you!