I will try to make some rudimentary explanations about color representations. But I can not answer your final question if one copy-paste for your workflow is enough.
Color is not absolute, it is relative, and in fact, it is very device-specific.
Take one cyan water marker and use it on magazine-coated paper and on a newspaper. The information about the color is the same (Cyan 100%), even though the ink is the same, the color is not.
That is what color profiles (and color spaces) try to predict.
Normally, on print-oriented software, or at least oriented in the initial settings some visualization corrections are made. For example, a single channel gray only file is visualized as a lighter tone as a desaturated RGB file, because it is assuming some printed conditions, a single ink, instead of an RGB file that will throw several combined inks during the print.
Or the RGB colors could look less saturated and vivid because it is previewing the colors as they will render when converted to CMYK and printed.
But that is only the beginning. The visualizations. Then we have the transformations.
These are different ways to how a color will best fit together with all the other colors inside a new color space or mode. As color is relative to other colors there are different ways to squeeze them.
Will this grayish-looking black, should be transformed as such, for when new conversions come, it never deceives the viewer to expect a pure black?
So, probably (I am more and more ignorant as this answer progresses) you don't need any transformation, but the raw numeric data. So try changing the default settings on grayscale images to gamma 1.
I assume that when you open an image you should not convert to the new color profile, but properly establish a defined working profile setting.