Reading what you posted, I end up somewhat confused. I think a true sandbox would be the opposite of episodic.
In my current (sandbox) campaign I have to resist having story arcs run into each other as, although it is convenient, it would be unrealistic plotwise in most cases. Episodic, in my mind, would result in nice clean stand alone adventures with clear staring and ending points. Instead, the campaign resembles an epic fantasy novel (in my deluded mind at least), in that there is a sweeping campaign level plot which the characters tend to crisscross throughout their adventures. There are also many subplots, usually character based, which the group pursues from time to time.
Nothing keeps them from saying "Screw it, I'm goin' home!" at any point, although they generally follow the story arcs in most cases. The sandbox aspect comes into play more often when I need to revise things based on the outcome of the players actions. For example, I expect them to kill an evil vampire and instead they befriend him and use him to reach another goal (just an off-top-of-the-head example, this didn't actually happen).
So I guess sandbox occurs at two levels:
A) The story arc level
and
B) The individual adventure level
DM's can mix and match levels of sandbox to suit their style.