OK - I think this is the end of this matter. I hope anyway. And after all my testing and re-testing of the drive and the file-system etc., it really looks like the problem - on both machines - was the USB cable I was using. Though I've no idea exactly how old they were, the certainly go back a bit. So now I'm using a new one with that drive on both machines and things are working - so far at least - exactly as they're suppose to. Thank you guys, as always, for all the input. I think it's fair now to put a large 'Solved' notice on this thread.