Actually I suspect that Songbird won't download because I tried it on a tablet that doesn't have Bluetooth. Poweramp wouldn't download either (but I could get it from the Poweramp site).
It seems that anything which uses the stock Android media scanner has a bug with album art. So far the only players I've found with their own scanners are Poweramp and Rockbox and Rockbox hung in the middle of scanning.
Next question: All screenshots I've seen of the Galaxy Player have a "Music" icon on the screen. Is this hardcoded to run the stock player app (thus requiring a second click through Applications before I can run my own) or can this be changed to run my own app?