Actually there is precedence for a woman wielding Mjølnir.
Irrelevent and not the point.
Even from its first appearance in Journey into Mystery, it's had a creed etched into the Uru of the head;
"Whosoever holds this hammer, if he be worthy, shall possess the power of Thor."
Correct
Beta Ray Bill
I own the issue where Beta Ray Bill first appeared. Thor Unleashed run under Walt Simonson was the best ever written for Thor.
However, when Beta Ray Bill picked up Mjolnir, HE WAS NOT THOR!! He was Beta Ray Bill before, and Beta Ray Bill after. Yes, Eric Masterson assumed the role as Thor, but very few people knew. It was largely a secret in fact.
No one is going to confuse Jane Foster Thor with Thor Odinson. Furthermore, when Foster first picked up Mjolnir in another multiverse she was Thordis, not Thor. She could have taken on the name of Torunn, which is a name not used in Marvel 616, but still part of the Thor expanded lore.