Happy to hear Mandy is doing well.
I would want a definitive diagnosis if my dog were in this situation. I wouldn't rely on BATs alone. It might be that there isn't a liver shunt. Could be MVD as MauiGirl posted in another thread, and Jeanie posted right below her that she had the same experience with her pup:
http://www.yorkietalk.com/forums/4426030-post8.html
That would give me great peace of mind, although still not a cakewalk.
In terms of anesthesia, I've read here of many cases of dogs with various ailments including compromised livers/LS who have surgery. As long as the specialist knows in advance, a special protocol is tailored to make anesthesia safe. Same with humans -- that is why the anesthesiologist often meets with patients before surgery.