I don't really know anything about this at all but I wanted to bump your thread so hopefully someone will give you some opinions.
If I was to have an opinion though I would do both at the same time so you both only go through the process once because as well as all the things you mentioned it also means that you won't be playing it all through you mind again in the run up to the next surgrey. JMO.
I know you will make the right choice for Tatum because she is your baby and you love her and know her better than anyone else. Go with what your gut feelings are.