I have now solved this, and thought I would put the rather simple solution in case it helps anyone else.
I discovered that it was not always left that was stuck down, sometimes it was up. Given that I had removed the keyboard and it was still doing it, I figured it must be thinking there was a joystick plugged in and was getting a bit mixed up, so I plugged in an old joystick, and on the next run, everything was fine. Removed joystick and it went bad again, so confirmed this was the issue.
So, with the joystick plugged in, I went into the mame menu, general inputs, and went through removing any reference to a joystick input, reverting them just to keys.
Removed joystick, and now all is well.