Have got back into the office (after a 12-day flat renovation project!), and made the client's new website live with a fresh installation of 3.4.
I've edited the bbparser.php file as instructed, and it now works!
Also tried a small change of my own ... used _BLANK instead of _NEW , and now I get a new window for each click-through (instead of them appearing in the same one) - great!