Rik- nice! Sounds like a lot less work than I just went through!
For Garfield, you may just need to tighten the two screws that are top center of the PCB- they squeeze the zebra connector tightly between the LCD and the PCB. If that doesn't do it, then you can unscrew 6 screws and pull off the zebra connector and clean it, the PCB and the LCD pads with alcohol.
If you do take it apart, please scan the PCB and I can check if the test pin is easily reachable, and we can document the LCD and button connections. I scan both sides of the PCB and then flip the component side horizontally and load the pics as 2 layers in GIMP. Then I add another layer and color traces to help follow them around.