I’ve just seen this on 35mm, and I can tell you the 2013 MGM Bluray looks faithful and much, much closer than your regrade. Visuals of course are only one thing, the original mono mix is obviously nothing like the bluray - but the sound on the print is absolutely thumping.
I’ll post some examples (regrade on top, 2013 MGM Bluray on bottom):
This is how it actually looks on a 35mm print:
The re-grade is too dark and has turned the background navy blue where the backgrounds are often cyan or green.
One of the scenes in the film where the background is very obviously green and not blue or cyan is when Sarah is driving through the tunnel, I just checked the bluray and sure enough it looks correct:
That’s exactly how it looks on release prints, and the road looks green as well as it does on the bluray.
The colour cast has been removed in the regrade, but this looks moreorless accurate:
Furthermore I don’t remember seeing a single night scene where the background looked so neutrally grey.
Rear-screen projection future war:
These scenes looked really amazing, and felt very intense.
The bluray looks fairly accurate. While it’s impossible for me to say for certain for every scene, what I can say is that most scenes like this had at least some cyan in them and did not look as blue as the regrade. It was also quite easy to tell this is a back-screen effect on film from the way the background is out of focus - nevertheless it still looked great.
Terminator enters police station:
Once again the regrade looks, to my eye, off. The only thing wrong about the bluray is that I’m pretty sure in that shot you could not see through the sunglass lens on the print (but you can in other shots). This is because prints don’t have much detail in the blacks.
Terminator in front of sugar glass:
The regrade is wrong. The bluray looks faithful. There are no scenes in the present (1984) that look as blue as the regrade, the only one that may have looked more blue are future war scenes, although I hasten to add many if not most of them had cyans or greens in them. The colour timing on the print was pretty consistent.
This is all largely in-line with what kaosjm reported in 2017. The future war scenes, some of them were “more blue” than the present, but virtually all of them had teal, cyan, or green in them. The scenes that were the most blue were the rear-projection scenes, but even they were not as blue as the regrade.
Visually speaking the bluray is remarkably faithful. Sound is another matter since it doesn’t have the original mono mix.