Gosh, I think it's looking really good! If I was looking at this photo for the first time, having never seen any other version, I wouldn't think anything was amiss.
Great! Then you don't need to do anything in Color Settings. Leave that window alone.
Now that you've saved the ICC file in the library, just soft-proof as normal: https://www.damiensymonds.net/2010/03/bit-about-soft-proofing.html
Yes, I know.
Earlier in the thread you said that they don't require you to convert your files - you can send them in sRGB as normal. Is that still the case?
Sometimes I find I have to take the scale down really small - like 20% or something - so I can get the gradient centred exactly where I want it. Then take the scale back up again.