thank you for your thorough report!
To start with, yes, your firmware is up to date. Your REX unit is one of the first shipped from the most recent manufacturing batch, and the difference between firmware versions is that the 1.1.4 works with a small design change in the new batch. (And of course it works with previous batches too.)
The tracking accuracy and precision that you achieved is better than you’d expect for most people. Nice! But be aware that most people don’t have as good accuracy and precision as you do when designing your app. A less accuracy-demanding user interface would spare you from having to sit still, dead center in the track box, too.
The experience that you had with the demo software sounds a lot like an offset error to me. I totally agree that it’s awkward to try to compensate for those errors by looking “in nirvana”. The question is why you’d get this kind of error in the demo app, when you don’t see it with the trace gaze function. I’ll have to investigate.