This morning I got a 'proper' Alinco programming cable (the correct wiring, not an Alinco part) and tried it with the programming software. The cable is USB to 3.5mm 3-pole jack plug and is a standard USB to serial adaptor. The ring of the jack plug has 2.8 volts DC on it (this is the data connection). Connected that to the Alinco speaker/mic converter cable through a 3.5mm/2.5mm jack adaptor.
I still got an error message in the programming software when trying to connect to the radio.
Using Filemon I checked whether the software was missing any DLL files (the old Puxing 777 5-in-1 software needed MSFLXGRD.OCX to work and this isn't part of a standard Windows install - it was included with the Yaesu VX7 programming software so if that was installed then the Puxing software would work). The Alinco software was trying to open MSCOMEN.DLL but the file was missing from the Windows\System32 directory. Downloaded the missing file but this made no difference, there was still the same error.
Next I tried copying the firmware to the radio, to make sure the cable was working. Downloaded the DJ-G7E firmware updater but this said the region was wrong. So I don't have the normal DJ-G7E. Tried the firmware for the universal model DJ-G7EG and that worked OK (a search for the DJ-G7EG returned mostly German results so I guess the G is for German).
Installed the correct version of the programming software for the universal model DJ-G7EG and it connected to the radio (very slowly). It takes about 10 minutes to read the data from the radio (and that's supposed to be at 57.6Kb/s!).
I bought my DJ-G7E(G) from Nevada.
With this software you can export/import CSV files which makes editing memories a lot easier (sorting them by frequency, finding duplicates etc.). This is better than the Icom IC-E91 software which had no way of sorting them. Also the bank sizes can be changed from the default of 100 memories, which is good because I don't like memories in fixed banks, it wastes memories. My UBC3500 scanner is better, it has no channel numbers, only groups which can be any size (up to a limit of 2500 channels in total).