So the good news is the Blue LCD I bought on ebay is fully compatible with the Korg DDD-1! The model I went with is the HD44780, although it has slightly different dimensions to the original, so I had to get a bit creative with attaching it to the case. I also had to extend some of the wires from the circuit board so they could reach the solder points.
Unfortunately, my excitement was short lived as I managed to kill the backlight within a few minutes as the voltage was probably too high.
So, after ordering another replacement (Yellow backlight this time), I decided to put an inline resistor on pin 15 to reduce the voltage. A quick google suggested something around 47 ohm should do the trick, but the smallest resistor I had to hand was 100 ohm.
I’m happy to report it all works fine though, and with no annoying whining sound!
I’ve also replaced the main navigation / cursor buttons which are a lot more responsive now. The back-up battery replacement was a bit fiddly, but I’ve done that too 🙂