Ok I gave up fiddling with the resistors ... at first the 'inverse' of your idea seemed to work Norbert – by connecting the ground first and then the positive the ESCs armed correctly 4 times in a row. But then I tried a few minutes later and the ESCs refused to arm! I bought a selection of low value resistors this morning, and whilst a 12R resistor actually seemed to work most reliably (I tried 1.5, 3 and 5R as well), there was still an unsatisfactory number of failures.
So I went back to an earlier idea in this thread of being able to switch the AQ on after the ESCs have entered their 1Hz beeping mode – I simply put a chunky switch in line with the power going to the AQ. I will leave the current 10R resistor in-line with the balance plug as it will protect my XT60 connectors from degrading due to spark erosion, and to power up I just flick the switch as soon as the ESCs start beeping. It's worked every time without fail so far.
Not quite as neat a solution as I'd hoped for, but at least it works reliably now.
Many thanks again for your ideas guys, it felt like I wasn't alone in my struggles!
All the best David