Concurring that this all hypothetical;
Assuming the masses can feel(?) the curvature of the space.
Could G be a potential energy when they are motionless and therefore the masses remain motionless? Then if one mass is set in motion in any direction would the two masses eventually come...
Although very interesting, the thread on detecting motion was based on the assumption that G is like an attractive force field (which MAY be the case if CERN detects gravitons). I was looking for some thoughts on the motion or lack of motion for the masses if G is only manifest as SpaceTime...