For objects moving away but not directly away in our light of sight, could we take measurements from different parts of the Earth and compare the readings to figure out precise velocity?
In principle, measurements taken from different places on the Earth would be seeing Doppler effects for different components of the object’s velocity, and so you could use them to improve your knowledge of the total velocity. However, in practice, the objects we observe are so very far away that there is negligible difference in the velocity component as seen from different parts of the Earth.