Closely but not identically. I’ve yet to see an image or asset that was designed for SDR look identical or even close to identical in HDR mode/colourspace on my Windows PC. So that might account for at least some of the difference.
The solution to this might lie in manual calibration and tweaking as you have embarked upon but with so many things there are tradeoffs.
Maybe if you had a brighter display things might have been better after calibration.
@MajorPainTheCactus seems to be getting stellar results on his hardware setup though but maybe his equipment might be not be representative of what the vast majority of users have access too.
I would like to see more feedback from users to gauge what kind of experience people are getting from this shader because so far it seems like some are getting great results, others not so good and for others something always seems to be missing.
Maybe part of the issue is that the expectations and standards might be a little different for this shader in a sort of uncanny valley kind of way.
The concept is sound and has been proven and the potential is there though but I think the userbase needs to grow so we can see what sort of awesome presets and photos other users come up with and start sharing with the wider community.