This is just my opinion, but I think the filing had more to do with Illinois politics and less to do with judicial strategy.
The gun control advocates made 3 runs at recreating the existing Illinois UUW law piecemeal and they failed. Last week the ISRA came very close to passing a shall-issue concealed carry, but some last minute manuvering by the antis stripped off a few votes.
But it looks like they expending the last trick they had and all indications were that the bill would pass if heard again. There was a lot of pressure on legislators to pass a bill before the 180 day stay expired which I think is in 39 or 40 days from now.
So their backs were up against the wall and by filing for cert, they may relieve that pressure on legislators if the extension is granted