PT Ch.1 opens "In the blue light of July pre-dawn" while SG was in February of that same year.
Harry does say at one point that he'd been a full-time dad for "well over a month" leading some of us to initially think the gap was smaller. I'd guess he's not counting "full-time dad" as having started immediately, but rather after he actually started investing the Time (and maybe getting a place to stay that's not known for driving people insane or being inaccessible for half the year. Or a car).
