My LCD screen is working!
Great, great, great.... I'm so happy this is starting to work well!
I don't have much time explaining what I did, but I must give credits to EnergyMicro (again) for their outstanding documentation and code library. Last weekend, while not having any hardware, I dug through AN0057 (EFM32 Segment LCD), and the description of what needs to be done to driver your own display, in combination with the source code is very good. I didn't fully grasp all concepts last weekend, but now, with some hardware, I was able to get the screen running within an evening. Very happy with that, I can just send an integer to the screen, and with a bit of tweaking it displays all numbers from -9 to 199. Cool!
For those interested:here is the code, most modifications are in segmentlcdconfig.h
Powering the device
Because I don't want to keep a boiling pot of water next to me all the time, I'm now powering from a power supply. Because the needed input voltages are so low, I just used a 100Ohm/15Ohm resistor divider to power the device. Not very efficient (most power is dissipated in resistor between Vin and GND), but at least I now have fine control over the input voltage!