I ended up doing this a bit differently. I did sweeps for the corners as per your suggestion, but then I custom made the inside using a copy of the main side, then doing blends between the two to connect it, then again around the lip to connect everything up. I then selected all and did a join (probably not a good way to do it, but I deleted everything else anyway). I ran into another problem though, with good ol' fillet. Try filleting the shown edges and look for the magical disappearing object!



http://www.dukecg.net/GinkoVase_02.3dm