Hi Torquil,
Thanks for the approach! I wonder why you normalized G to be 1. Using the usual 6.63 10^-34m lowers r if we keep in the mks system. Also why a year? Why not a second? For that matter (no pun intended), at those scales, 1 second is pretty close to eternity (the smallest time scale...
Theoretically, the range of gravity is infinite. OK. But the nature of the fabric of space has "building blocks" (Planck volume?)
So while a localized body of mass/energy distorts space-time, the distortion decreases away from the body. I would think this has a practical limit. Just as energy...