Everything you say is correct except for adding up all the lengths to become one. They are all parallel runs so the longest run is all you would need to calculate for, as you will be splitting the circuit and going three ways under the seat pan someplace.
I used a number 18 awg for strength, even thought technically the wire could be smaller.
That being said, the fuse protects the wire. You could fuse the number 18 awg higher, but in this case you shouldn't need more than 5 amps. I would fuse it at that.