Sort of (and it's my fault for not being clearer). The power supply and the separate electronics control box is in the middle (over the stove/fan). I spliced after the control box (sorry if that wasn't clearer earlier). One wire from the control box runs leftwards to the left strip and the other wire runs rightwards to the right strip. The two strips are, thus, independently connected to a single control box which, itself, connects to the power supply with original cable.
That would work too. The only drawback would be that if either set of solder joints is not perfect, then the strip furthest away from the control box would exhibit defects. It would be harder to troubleshoot.