They tried on the moon, but there does not seem to be an assumption that this is limited to the moon? So one could obtain a position anywhere in earth's orbit, up to heights of 380.000km? 1.5km accuracy is impressive then.

Apart from the attenuation from distance, I would expect that the navigation sallellites point their antennas mostly downwards to earth, but you might find some that radiate outwards. I don't think you can expect to receive from half the satellites though.