One thing I've spent some time thinking about is whether it would be possible to use atomic clocks to get a better measurement of the gravitational constant G. (G is by far the most poorly known of all the fundamental physical constants.) The idea would be to build a sphere whose mass is very precisely known and place one clock near the mass and one clock far away. By measuring the gravitational time dilation you could infer G. As I recall from my order of magnitude calculations, atomic clocks would have to improve in accuracy by four orders of magnitude or so before this would be feasible. So it would still be a long ways off.
Good point! The research group is still working on refining their system. So may be they will have another breakthrough in a year or two, you never know!
