Base Feed Rigid High Tower Model
The problem with the Base Feed High Tower is that as bodies rise, they lose angular velocity. If the tower was held rigid - for example if it was constrained within a rigid tube - every body would always maintain the same angular velocity (although this would apply lateral forces to the sides of the tube).
In this applet, a rigid tower is simulated by transforming X-Y velocities to radial-tangential velocities, restricting the tangential velocity of any body to planet angular velocity times radial distance, and then transforming the two values back to X-Y velocities. Fed from the base, this pulls up material faster and faster. Oscillations within the tower eventually result in collisions between bodies, breaking the cables, so that the lower portion springs back down onto the planet, and the rest continues to accelerate outward.
This demonstrates the siphon, but an uncontrolled siphon which accelerates and destroys itself. The next step must be to try to restrict this acceleration, and produce a siphon which feeds up bodies at a steady rate.