@Claes - really nice comparison.
I think soft proofing to get a nice print on the inexpensive paper would be challenging. Recently I was reading about painters using hue changes to indicate shadows and highlights, back when paint palettes were very limited. Could one do something similar to make a nice image on the inexpensive paper? Maybe use hue changes to indicate tonality changes in the bright magenta flower? Perhaps bluer in the shadows and more yellow in the highlights? After lowering overall saturation of course. The blue flowers also would need their saturation lowered, and perhaps the entire image could be recolored so to speak, with less saturated colors, with more emphasis on hue changes to indicate/augment tonality changes. Just a thought!