As this project picks up steam, new insights emerge. Since the useable width of the 80cm cabinets is actually 76cm, three strips of 25cm will not fit, lest we eschew the power connection, but that would render the strips useless, so we need even less strips!
I also had to figure out how to hook it all up and make it flexible, in order to switch to optics later on, in case the switches give out too soon. I'd rather go that route in the first place, but a lack of time made me put that idea on the back burner.
The first few cabinets have been fitted with wiring: I routed a slot on the side of the cabinet to guide the wires through, so that nothing is visible, apart from a short bit of wire to the strips. Everything is ultra low voltage and draws next to nothing, so there's no chance of heating up.