I've run the Nero software again on a new blank DVD+R disc and unfortunately I'm not given the option to close the session. I've run two burning sessions, as before. The disc shows as having two sessions on it, which is correct. But it won't show me the contents of the second session, only the first, which it displays just fine (files all display just fine.)
All I'm allowed to select is a tick box against "Allow files to be added later (multisession disc)" before burning.
I've been ticking that.
Then it just allows a "Burn" button press (apart from some irrelevant other buttons) and off it goes on a burn.
Then thats it!
I'm sure I'm specifying DVD media and that the drive I'm selecting is correct.
The drive supports writing to all DVD disc types.
As an added simplification, I've firstly removed all the other manufacturers software which does burning (Roxio, in this case).