Your own answer is really close, but there is a better way...
You can use ADJUSTMENT LAYERS to strip the unwanted channels out of each layer rather than deleting them by hand. This is non destructive so your file can stay layered and 'live' and it will be easy and quick to implement additions and changes. There are a couple of different adjustment layers that can be used for this; I've gone with CHANNEL MIXER, but CURVES would work just as well, for example. Whichever you use, you just need to remove (make black) the two channels that you don't want in each case. As you found, the layers need to be set to sccreen.The key is to make sure that the adjustment layer is only acting on the layer directly below it by selecting the 'clip to layer' option.
Below is a screenshot showing the set up in layers and the resulting channels. I'm using CC so the appearance of the palettes and the wording of the options might be slightly different to those that you see, but hopefully this will be enough to guide you to the solution.
If you create a template PSD file with the appropriate adjustment layers then you can just drop your components in to the appropriate locations in the layer stack each time for a quick and easy workflow.