What a tricky question as the choice of working profile ?
Some elements to bring water to the mill!
You would think that the better the profile, the better it is, hence the choice of Prophoto.
But we are not sure that the data of the device fits well in Prophoto, moreover Prophoto contains colors outside the visible spectrum.
the use of Prophoto will lead in some cases to make the sliders inactive when we refer to the luminance RGB, whose blue coefficient is close to zero.
Today the majority of the screens has a gamut close to srgb, and in some rare cases AdobeRGB, can be in some cases a little more, but one is very very far from Prophoto
Today the majority of printers have a gamut lower than srgb, and in some rare cases some colors can reach Widegamut, but also one is very far from Prophoto
When one calibrates his camera, to elaborate a profile (ICC or dcp), in the majority one uses a colorchecker, whose almost all the colors are close to srgb.
All the colors outside this case are extrapolated and therefore probably wrong, except if we use a target rich in colors close to widegamut (the maximum of printers).
Moreover it is not because a camera profile (matrix or ICC or DCP) is wide that it contains all the colors and moreover the renderings are probably nonlinear.
In synthesis and not in conclusion I think that choosing another working profile would be interesting for example RC2020, or Widegamut.
My preference is towards WG which has a superior size superior in the reds.
Now as for the best way to saturate, it depends …
if you are a Cartesian scientist, you will choose Lab, who also has a Munsell correction, from a mathematical point of view the rendering of the colors will be almost perfect
if you admit that our brain and our eyes do not respond only to strict laws, but that a part of subjectivity exists, in this case prefer Vibrance or better still Ciecam.
I did not add at the end of the Ciecam a module Munsell, we could do it but it would go against the meaning of the work of the researchers
But what is on it is that the worst method is saturation in RGB modules (exposure)