This story is good, but Neptune is not really very dense.
Neither can Neptune be the answer since the bodies aren’t close enough to the dense, blue giant.
The density of Neptune is 1.64 gr/cm3 while the density of earth is 5.51 gr/cm3. Neptune is denser than water, but our planet is roughly four times as dense as that distant blue marble.
Neptune is denser than Jupiter and Saturn, though. In fact, the density of Saturn is 0.687 gr/cm3, so it’s the only one of the gas/ice giant planets that’d float in a bathtub, if you had a really damn big bathtub. (Water’s density is 1 gr/cm3.)
Neptune’s gravity is only about 14% stronger than Earth’s, so if it had a surface to stand on you’d barely be able to tell the difference.