Embed Camera Profile fails - Conversion to ProPhoto makes picture lighter

Hello,

I am trying to export images in their original *.icc profile (custom made) but it seems to be impossible as if I set my ICC Profile as input profile in the base characteristics panel and "Embed Camera Profile" under ICC Profile in the formula panel it only works if the input ICC Profile is the generic one for the camera suggested by CO or one of the seven profiles located in the Effect section of the base characteristics panel.

I've found out that the topic has been brought up already 13 years ago but, at least to me, it seems like it hasn't been solved.

Why to export embedding the original input ICC Profile? Because if I export converting to ProPhoto, AdobeRGB, or you name it, the resulting image will ALWAYS be a little bit lighter than what I see in capture one. Always. So my hope is that converting the image to ProPhoto in another editing software will correct this other bug of CO that has been known for year and years.

Any ideas or suggestions?

Thank you very much for your precious help.

Ale