Well, your suggestion seems to work, it looks much closer to expected result.
In my original post I used exactly the same scene on both 5.0.3 and 5.1, and while it worked fine on 5.0.3, it resulted in weirdness on 5.1. So something did change in 5.1, and now that I think about it, the default size seems way to small (as in it would clip with most things in a regular scene). So it remains a mystery to me why it worked at all before.
I have more troublesome scenes with HDRI on 5.1, so I will do more testing to see if increasing the size fixes all these issues. In one of them, for example, the character is all black on 5.1 but works perfectly fine on 5.0.3.
Thank you very much for your help.