Rapid drops result from high temperatures. Rapid slumps cause a thinning of the glass at the shoulder where the glass turns over the inner rim of the aperture. The pattern is distorted and the colours are also diluted. And a relatively large rim is left around the fired piece.
A much slower rate of drop spreads the strain of the slump over the whole of the unsupported area of glass. This tends toward a bowl with a gentle slope toward the bottom, reduced distortion of the pattern, maintenance of the colour densities, and a more even wall thickness all over the piece.
The slumping temperature for a shallow angled slump is less than that used for normal slumps, and takes a lot longer – up to five hours typically. This means that observation is required at intervals, say every half hour.
A starting point for the slumping is around 100ºC above the annealing temperature for the glass. So for Bullseye and System 96 the temperature is about 615ºC. If after the first half hour, there is no movement, increase the temperature by 10ºC. Check again in another half hour and if the slump has begun, leave the temperature at that level and observe at the half hourly intervals until the desired slump is achieved. Otherwise, increase the temperature by another 10ºC with the check after half an hour, and repeat until the slump has begun. After you have done the first one of these with a particular size of aperture, you will know the temperature to start the slump.
The temperature you need to use is affected by the size of the hole. The smaller the aperture, the higher the temperature will be needed. But be patient. If the temperature is increased too much, you will get the thinning of the sides that you are trying to avoid.
Additional information on aperture drops can be found in this series.