I have not done an LSx engine swap, but yes this has been done many, many times. I am sure a few of those that have done the swap themselves will chime in. In the meantime, I would suggest checking the LSx swap section for some answers to your questions.
http://www.67-72chevytrucks.com/vboa...ysprune=&f=206
One thing I can tell you, is that it will be a whole lot easier to use the trans that was behind the 6.0 originally, rather than trying to make a 700R4 work.
Oh and FYI, a 6.0 is 364 cu in not 350.