How small do you want the cone points to be? If you’re really pushing it, something like a 3/8” high-strength steel rod, epoxied into a center bore, should give adequate strength. I’d bore all three pedestal components through. Then the rod itself would be serve as an alignment pin for glueup. Depending on how you plan to attach the top, you could either turn between centers, or leave the steel rod proud and chuck directly onto it.
I’d also turn the down the small ends of the cones last, and do it at very low speed — that pedestal geometry is going to want to whip like crazy. Come think of it, turning the components individually and then assembling them onto the steel rod might be more practical. You could even use threaded rod, and simply bolt the assembly together.