Defesphere

Instead of squatting atop a bowl which puts cold water perilously close to personal discomfort, replace the bowl with a large sphere, maybe 2m radius. Otherwise it's a standard flush toilet - marginally increased water volume, standard seat, etc - it's just overly huge. The spherical shape means that errant material never reaches the sides and the ~4m distance means that, aside from being installed on the lower floor and accessed from the upper, the prospect of frigid splashing surprises is tremendously reduced. Cleaning might be more difficult, but imagine the wonderful dinner party conversations the mysterious globe in the restroom would inspire!