But at least I have some tangible evidence against the theory where as all you have is posting style.
You don't have tangible evidence. In what way is it evidence? You're talking about different IP addresses, which are ridiculously easy to fake.
This isn't just her posting style. It's a pattern of behaviour. You seem determined to not be wrong on this, even though you don't have any real reason to be so sure that they are different people.
Even the information you verified is irrelevant, as you seem to have conceded.