My understanding (based on a quick scan of
this PWI lecture, first linked upthread) is that the northern box abutment slots in under the current bridge, so it can go in once the pile caps are done. They even intend the walking/cycling path to be routed through it, while work is proceeding.
However, the southern box abutment needs the embankment moved out of the way before it can go in. Once that's been done the abutment (cast on site) drops into place with stitching added, which is fairly quick. So you might as well slap the deck in place during the same blockade, while you are also filling in the gap in the embankment. The old southern abutment can be flattened while the embankment is being dug out; none of that has to create a load-bearing surface, nor does what's in the new road space have to be taken right down initially.