Having failed to split moderate diameter dogwood, I guess the only option is the bandsaw. Is it feasible to rig a way to orient the cut line with respect to the pith at each end of the billet?
How many do you want to cut, what length, and what does moderate diameter mean? Can be as simple as snapping a chalk line and making a long v-block that will be a one time fixture since it will get ripped too. Or as complex as an adjustable sled that rides in a miter gage slot.