Really? She has a name, and she's a saint?
Yes, definitely. I certainly agree. Jesus was looking for her. He cared, and she knew deep within her being that she was loved!
Others including myself, have wondered about the seeming holes in the Woman at the Well story. Those better educated than me pointed out the same things you have. I don't think the solutions you presented are imagination or wishful thinking. They are the only plausible answers. More important was the woman's reaction proves that like Mary Magdeline, she got it. She really got it!!!!
Except that her having five husbands directly mirrors the history of the Samaritan people and their alliances with five different pagan nations. Part of the story is that Photina is the perfect representation of her country, because she's committed the same sin her country has. Christ isn't just coming to her, he's coming to reclaim her people.
There's also the verse, "and the one you're living with now is not your husband". That seems to imply some guilt or sin on her part, if she's living with a man outside of wedlock.
I don't deny that trauma might be part of her story. Maybe some of those marriages failed because of abuse or she was widowed. But there's more reason than just a modern judgemental lens to see her story in the light it's commonly presented in.
Either way, the story makes abundantly clear that she's seen as she is by Christ, that she's loved in the midst of that, that Christ restores her dignity
in the midst of shame, and that the conversation moves her to call as many people to Christ as she can.