I have asked around a bit: the statisticians use CyberSports Basketball which has a "Game Monitor" feature. This can be run on the same computer, or on another over a network connection (can use a wireless card or not).
Game Monitor can publish a live boxscore at a specified interval (e.g., 30 seconds) via FTP to the web. From that, I have my ABL/Blitz Stats scripts that can parse the boxscore on the fly and output something suitable for the bigscreen (e.g., player, points, rebounds, assists, shooting stats, fouls). If the NBL don't want the club publishing that live boxscore (or they already use it for their own live scoring), you set up Game Monitor on a second-hand desktop box (everyone has one lying around) under the desk publishing it to a local FTP location, and then parse the scores on that under-desk box and output straight to the screen.
Cost: crap old computer for a couple hundred dollars, and my time. Offset that with stats sponsorship (I'll source it even), and it's free.