Hi Jesper.
Looks like you have researched this well.
I'll add a few points that I learned along the way as I have exactly the same gear installed in my car.
I didn't find the need for connectors anywhere, although I used a couple of terminal blocks under the seat near the LMA-3 to help organise my wiring.
I mounted the LC-1 just above the relay panel at the left side of the engine bay and ran all the cables into the car from there. They weren't long enough to go all the way so I bought some similar multicore shielded cable from Radio Shack and added about a metre into the cables. I soldered all joints and used heat-shrink tubing on the separate wires and around the bundle.
Wire size: I am also not familiar with wire gauge sizes, but the smallest size is adequate for all the signal wires. The earth and power to the O2 sensor might need larger cables - I'm sure someone will confirm.
I added a few extra wires into my loom from the engine bay to the terminal blocks for future sensors as well.
Here's my wiring diagram which might be of use. All colours are as per the Innovate parts.
