Yeah, it sounds like Sadie is a combination of the things you're NOT looking for in a dog. But, hey, better to know now when you're only fostering than if you'd adopted or bought her permanently.

Italian greyhound does sound like a very good choice (especially with the plain greyhounds being rather large...). If you can't find one, Whippets are quite similar in size and behavior. On the outer edge of that size/activity level/look/temperament are the Miniature Pinscher (a bit more on the "hunting" side) and the Manchester Terrier (I know--a terrier, but they aren't quite as typical terrier as some).

I hope you feel better soon!