If I didn't have the vessel head, I would have built a hexagonal grill using a sheet of 3/16" thick carbon steel. The bottom would be flat and approx, 1/2"- 1" larger in diameter than the sides, this way you just do a stitch fillet weld to join the sides to the bottom and the two don't have to be bent as precise.
A hexagon is really simple to draw with a compass and has simple 60 and 120 degree angles. You can bend the plate easily by making a thin groove using a straight edge and angle grinder with a cut-off wheel. Make your groove on the inside, so you have a nice clean corner on the exterior. After you've bent all 6 sides and tacked it to the bottom, you can run a thin weld bead on the inside angles where you made the groove.
I hope that makes sense.