Has anyone been able to measure a difference in the energy density of Cosmic Background Radiation in a gravity well compared to zero gravity?
The problem is that the only gravity well to which we have easy access is the one that we are sitting in. While it's true that the combined gravity of the Earth and Sun will mean that CBM radiation reaching the Earth's surface is blue shifted, the blue shift is only a factor of about 1.00000002 and this is far less than the experimental errors in measuring the CMB.
We can't see frequency shifting due to gravity wells away from the Earth because the CMB radiation reaching us will have descended into those wells then climbed back out again, and the net frequancy shift will be zero. In principle we could see gravitational lensing of the CMB in the same way we see gravitational lensing of light, but the resolution of current CMB measurements is nowhere near fine enough to see gravitational lensing.