If the source document and the target document are the same pixel dimensions, you can use the "Image > Apply Image..." menu command. This will permit you to specify the source document, layer and channel that you want to insert into the active channel of the target document.
So, with the target document active, go to the Channels tab and select the channel into which you would like to insert the layer from your source document.
Go to "Image > Apply Image" and select the source document, the source layer and the merged channel (channel should not matter). Here you can also select a blend mode, etc. but set that to Normal for your purposes.
Hit OK and the target channel should be good to go. This way you don't have to keep switching between documents to Copy and Paste. Just remember, Apply Image only works for documents that have the same dimensions.
As for why your old way is not working, I don;t know.