I became interested after reading this passage about Mondino's female (assistant) anatomist, and wondered how an Italian educated women can get hired for a job in the middle ages.
She became most valuable to Mondino because she would cleanse most skilfully the smallest vein, the arteries, all ramifications of the vessels, without lacerating or dividing them, and to prepare them for demonstration she would fill them with various colored liquids, which, after having been driven into the vessels, would harden without destroying the vessels. Again, she would paint these same vessels to their minute branches so perfectly and color them so naturally that, added to the wonderful explanations and teachings of the master, they brought him great fame and credit. [Cronaca Persicetana]
Unfortunately, the answer is "what job market." The two major ways for a woman to get a significant/academic education in late medieval Italy were as a future nun or to have a really, really rich father who wanted to show off, and neither of those led to getting a job.
That doesn't mean they didn't work, of course. For the nuns of San Jacobus Ripoli (Florence), their scribes' external commissions were so integral to the convent's economy that they bought a printing press in the late 15th century. Italy's women humanist stars sometimes ended up running their entire extended families' political and economic interests behind the scenes. But they didn't--couldn't--go out and just "get jobs."
Unfortunately, that includes jobs as scientists and surgeon's assistants. The Alessandra Giliani story you quote is apocryphal--the techniques described (dissection and illustration) did not exist in the Middle Ages. There's no outside proof of her existence, either. The Cronaca Persicetana has never been found, and the story and its evidence first appear in the 18th century.
No surviving copy of a medieval book is NOT proof that it didn't exist. But it's relevant in this case because it was clearly not a 14th century creation. And modern scholars seem to agree that the "supporting evidence"--a tombstone epitaph--was invented by the 18th century author. :/
I wish I had better news for you, or that I could have confidence Giliani was just papered over by "nasty men being nasty," as my advisor would put it.