You realize that having people work double shifts to fill out a 4 shift rotation is essentially just running a 2 shift rotation?
Yup - but the point would be that the two separate working periods are shorter by half than the previous single one, which may be to the advantage of the ship in reducing short-term fatigue. And Jellico wouldn't be dealing with the long term, as his intent would be to secure the very existence of the long term through sacrifices made here and now.
We have to consider, though, that Jellico was also factually adjusting the number of crew involved in the various pursuits. He was e.g. removing engineers from the equation and placing them on "standby" security duty - in which case it might indeed be a smart idea to turn the three shifts into just two (as 1/3 of the personnel was lost), and then split each in half to combat the fatigue.