The only way to go is to go is slowly and by not sending a ton, ie inject genetic material into a rock that's already on its way, hope for the one in a trillion chance that it takes root somewhere. That we're so alone in the galaxy is proof of this.
I don't think there is any real advantage of matching velocity with a rock and transferring material to it, compared to sending your own spacecraft at that velocity.
A big rock with its own momentum is more likely to come down on the surface (wherever it is) intact enough. But yeah there may be other ways to spread our seed. My point is that it will unpropelled for most of the journey, and a seed not an ape.