Having given some more thought as to what would be the result of the running the above test again, made me realise that you could reduce any risk to the transmission caused by running with the kickdown cable disconnected by doing the tests with the rear wheels off the ground. (As long as the car is still level, and well supported and chocked.) But thinking further to what has been done before, we know the Governor is working to some extent because the shift 1-2 at about the correct speed, and that speed is reduced to virtually zero by disconnecting the kickdown cable. So from that I would assume from that the Governor valve is free to move in the housing, but there is a weight that slides through the centre of the valve, and continues to increase governor pressure after the valve itself has reached full travel. If the shaft that has the weight on the end were sticking in the valve itself it could cause problems at higher speed, so giving the correct 1-2 shift, but delaying or stopping altogether the 2-3 shift. Conversely if the valve were free and the weight were still able to move that could compensate for the stuck valve. It's unusual in that they don't give many problems, and when they do they tend to either work, or not, rather than half-work as in your case. I think it's unlikely that both are stuck, but if you get to the stage of taking the governor off, you're going to see one way or the other.
So you can run the test again if you want, but I can now see a possible cause within the Governor that may make removing it and having a look worthwhile. Knowing the Series number of the gearbox may be useful as later governors can't be dismantled in the same way as earlier ones.