That said, given the nature of your dependent clauses, it sounds as if you need she/I.

I’m willing to concede that there might exist a situation in which her/me would be appropriate, but I can’t actually imagine one.

Basically, it concerns a sentence of this form:

(Independent clause): X buying cranberries, Y buying sun-dried tomatoes.

Where X is a young woman and Y is me.

Which of these is correct?

* she buying organic cranberries, me buying sun-dried tomatoes
* she buying organic cranberries, I buying sun-dried tomatoes
* her buying organic cranberries, me buying sun-dried tomatoes
* her buying organic cranberries, I buying sun-dried tomatoes

My first instinct was (her/me), but I decided (she/me) made more sense upon further reflection.