Even big machines will have some spring. One lathe I run at work is a 22"X 90 Kingston. Nice heavy machine. Use a 1" carbide bar. Had a guy running parts that needed a .003 tolerance on the id. He came to me and wondered why when he took the finish pass, it was always over size. What I do is retouch off with the tool and dial in from there for the finish, if needing a small cut. When you go just from measurement and dial it in from the last setting, it don't always work well. Try to take the same depth of cut each time, checking actual metal removal, and take that same cut as a finish cut. Usually will result in a better finish as well.
I would not run my tools below center at all. Changes cutting geometry, and the potential to break the tip of the tool increases as well. Just my .02