I have updated some of the missing key combinations to try and fix this.
I appear to be limited to two allowed combinations per key part however, so there are a few combinations I cannot currently set up both ways.
If we call the four parts of the key A,B,C,D from top to bottom and for joined up parts we add letters such that the whole key will be ABCD. Then I can set part B+A=AB and part B+C=BC but I cannot also add part B+CD=BCD as this exceeds the 2 allowed combinations for part B. I can however set part CD+B=BCD and part CD+AB=ABCD as there are only two options for part CD.