Most research on parachute stability has already been done. A conical type would be the simplest to construct, just make a 12 gore flat canopy but leave 2 gores out. That should get you the stability that you want without too much trouble. The long answer is there are a lot of factors that can affect parachute stability, shape being only one of them. Suspension line length, line count, distance between load and canopy, etc. Drop tests can help but for clear results indoor drop tests would be best. This eliminates air currents as a factor, this can be a big problem near structures.