Super post Exonian ...really good read and informative .
I'm glad you could make some sense of it.
I've just read it back after a couple of days and confused myself!
I've always thought tuning boxes work best with Diesels.
With a Diesel you just have to throw in more fuel which will then make more power (up to the point where you just get smoke) which in turn up's the turbo boost. Ok, it's a bit more complex with modern Euro emissions controlled Diesels with filters and EGR's but the same principle.
On a petrol engine the tuning box fools the ECU which is reliant on messages coming back from the sensors, which in turn means the ECU has to send modified signals to up the fuelling, boost and adjust the ignition so there's a very slight delay going on all the time under load. That's how VW can spot a tuning box has been installed, by looking at logs of unusual requests.
The pedal box is much more discreet. But it doesn't up the power, it just releases the power you already have in a more useable way when you're not using full throttle. You can set it to go from zero throttle to full throttle without burying your foot into the carpet too but that doesn't make for a very good road car set up if you ever encounter traffic!