As I have said before; I would get the engine problems fixed before spending any time/effort sorting the gearbox problems. You may well find that the slow shifting is due to problems with the engine. I presume that it is the upshifts that are slow? The bit of the upshift which I suspect you are saying is slow will be the time taken for the engine speed to reduce from the speed in the start gear, to the speed of the new gear. This speed reduction is done by the gearbox telling the engine to reduce its torque. If the engine does not / cannot reduce its torque sufficiently, you will get a slow shift. If there is a fault with the engine, then it may restrict the amount of torque reduction that is available to the gearbox. The engine tells the gearbox how much it can reduce the torque (from which it would be able to calculate the ‘shift speed’) so it may be the case that the gearbox has no fault codes, because as far as it is concerned, it is operating within the confines of the parameters available to it.
An ECU change may be the best bet (if you have had a reflash), but I would say that the best people to ensure that you get the correct model ECU and ECU software / calibration would be a VW garage. I’d be surprised if a 3rd party had access to all the detailed info about the spec of your car that VW UK would (although I could be wrong).
I have a lot of experience of the transmission on your car (DQ250), so whilst I’m not claiming to be an expert and to know exactly what is wrong with it whilst sat at my PC, and that I know best, that is my advice to you.