* Problem solved, I strongly suspect.
My stupidity truly knows no bounds and I owe AA a huge ‘fruity bun’ for wasting their time.
AA staff pointed out that they were seeing a ‘usb hub’ and asked me about it. I said ‘no’, I just have a straight usb cable from the Firebrick to the USB ‘dongle’ 3G NIC, but I had grown suspicious. I asked Mrs Weaver to fetch me the said cable. I had asked mrs weaver whether she had plugged in a usb hub and she said no, but in fact I had never seen the cable that Mrs Weaver had used. Looking at it the far end looks way too large and at perhaps 5m in length it has to be too long for the passive usb limit, no? So perhaps it is an active usb repeater. Maybe such things look like usb hubs to the upstream hardware. It only has one socket on the far end of it, so that’s why Mrs Weaver understandably didn’t consider it to be a usb hub.
Anyway, surely we have found the answer now, I suspect that either the amazon cable in question is rubbish or else it draws too much current from the Firebrick and so occasionally the voltage droops. Or there is a dI/dt problem, also causing a voltage droop. Perhaps needs a capacitor in a strategic place. Perhaps the whole setup would be ok if we were using an externally powered usb hub.