You are going to have the most mass and support if the headstock is over the legs.
If you are finding that the pieces are out of balance more often than not. And, your are not intentionally turning an off center piece.
You might want to work more on getting your piece balanced between centers before you turn the lathe on.
Likewise if your are using a faceplate, you might want to spend a couple of minutes finding a good point of balance ( between centers) before screwing the faceplate on.
Using a bandsaw to cut corners off of blanks, and to cut round blanks can also help a lot.
This can speed the turning process as you will probably be able to start at a somewhat higher speed and not spend so much time knocking off the high spots in search of balance.
With your new lathe I think you will find that it is pretty stable even with a slightly out of balance piece.
If it starts moving much then you have a potential problem that may be better solved with the lathe off.
I have never turned on a shopsmith, but I am assuming that your experiences with it are driving these questions.
Give your new lathe a chance, I think you will be impressed with it.