Thanks HairyFool, I ran Produkey as you recommended, and found a BIOS OEM license key that I did not have before. It ends with xxxxx-xxxWMC. Any idea whether this looks like 8.1 Pro key and whether it's HP specific?
(E.g. it could be potentially useful for an Acer upgrade from Win10Home to Win10Pro that they mentioned in the article I had linked. If it works, I would end up with running both Win7Pro on the original HP computer and an Acer Win10Pro using this other license... ?)