Come on, let's simply examine observable phenomena. The Earth orbits the Sun of either 8.3 minutes ago or the Sun of right now (or something in between).
Where ever that point resides, from the Sun of 8.3 minutes up to the Sun of this very moment, will let us calculate the speed of Gravity (unless Gravity can somehow be slow *AND* predict where the Sun will be in 8.3 minutes).
Consider two bodies -- call them A and B -- held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation.
Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So to the extent that that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity.