Of course gravity has a speed component, just as any other field. This problem is analogous to the problem of speed of current in an electrical circuit. When one closes a light switch in a room, the drift velocity of carriers (electrons) is slow enough that it takes an appreciable fraction of a second for any given carrier to reach the light bulb. Yet the bulb lights nearly instantaneously because the field propogates along the wire at the speed of light (a line of bb's in a straw may individually move slowly when a force is applied, but the one at the far end will move immediately because the force field propogates immediatly). Einstein and Hawking spent their lives attempting to unify gravity field behavior with EM fields and it is yet to be done. However, it seems that c is the limit and so gravity fields would propogate at c.
By the way, Ross, the oblique wavefront problem is analogous to shining a flashlight out the front of a ship moving at c. The beam front will still not exceed c due to relative length contraction and time dilation in the fixed frame of reference.