I bet when you were lower, your rear camber was closer to what the front was. That can make a big difference in balance especially if the tires are more camber sensitive.
A little bit of toe can go a long way as well. Zero toe in the rear could be a big part of the looseness, depends on your rear toe compliance (rubber bushings or PU?). Also try zero toe up front or even a tad toe out to tone down the yaw rate gain a bit. YRG is essentially a measure of a vehicle's response to a given steering input--the more your point the tires out of the turn, the lower your YRG. Meaning point the fronts out and the rears in if you want to take some oversteer out.
Softer springs could help but looking at how early the car oversteers during the cornering process is making me think that the main problem lies elsewhere. I could be totally wrong but that's what I'm reading in between the lines.