Thank you very much Coranda for your help.
Regarding your comments:
1. You are right. If I might add, to clarify: blending (e.g. normal, darken, lighten, multiply, etc.) with a custom opacity is the usual approach. As you said, most of the time the target is a single channel.
2. If I understand you correctly, the target layer is the only one being modified, the source should be left untouched. Both, source and target, could be either a grayscale layer or a channel.
3. As far as I know this is the case, yes. To be consistent, the blending algorithm should behave exactly the same, either as layers or inside the "apply image" window. When creating a layer from a channel, the pixel values should match exactly. Please note that this is not the same as PS "Image: Mode > Grayscale", were PS makes an average of the three RGB channels in proportion 3R-6G-1B (source: "Professional Photoshop" by Dan Margulis). AP might be using another formula, though.
4. I cannot check it right now I don't have a PS available. Nevertheless, please note that creating grayscale images from RGBs in PS is performed by averaging the three RGB channels (check point 3. above). If I am not mistaken (please correct me if I am wrong), what we want is exact value match, i.e. a 100R in the red channel, when converted into a grayscale layer, should be equal to 42L in LAB (or a 100R-100G-100B gray).