From Desktop to Mobile rendering: Color unmatched! (and that's a problem!)

Hello everyone.

This is regarding making a project that is able to output VR desktop (Rift, Vive) to Mobile VR (Go, Quest)
Playing the same Map on a Rift and a Vive ends up completely different color wise.

As a disclaimer, yes I know it’s very different rendering paths, BUT my project is particular (visually and I am trying to have identical looks)
I am nearly there except on the colors output.
My ToneMapper on desktop is at DEFAULT settings.

Let’s just focus on the colors.
Yellow is completely lost.
And it definitely shouldn’t be that way.

FYI, I use:
-OpenGL ES 3.1
-Tried with HRD on&off

A solution was to turn on “filmic Tonemapper on Mobile” (requires HDR)

Then it looks the same in the viewport, NOT on the Oculus Go.
(I can confirm that the F.ToneMapper works as I am able to tweak the settings, ie: saturation to go B&W)

The yellows just doesn’t match at all.
I tried to tweak every settings, I can’t get even far from it.

I have no idea why.
(My guess is: it’s turned off on the GO itself somewhere)

With Quest on the horizon, it will be great to have the colors rendering match from desktop to Mobile.
I don’t want to use film tone mapper on mobile (for performance), but the colors should look the same regardless.

What to I have to do to have the Mobile colors match the desktop one?
How come I cannot match the Mobile filmic TM to the desktop one?

Thank you!
(I will report back any findings, but so far after 3 days… no much)