[Gulliver]

Compasses don't work there.

Compasses work there. They point to the magnetic poles always. While the geographic and magnetic poles don't align and compasses must be allowed to point downward near the magnetic poles, they do indeed work. 

[Tintagel]

GPS satellites orbit the round earth.

What if those three satellite gps beacons were high altitude dirigibles, or antennas installed at military bases? Would GPS work then?

GPS satellites orbit the earth, 24 give full coverage.

You evaded the question.  What if?  For what it's worth, I do think there are satellites above the earth, as I've observed them.  I don't think they are at the altitudes reported, however.

[Gulliver]

GPS satellites orbit the round earth.

What if those three satellite gps beacons were high altitude dirigibles, or antennas installed at military bases? Would GPS work then?

GPS satellites orbit the earth, 24 give full coverage.

You evaded the question.  What if?  For what it's worth, I do think there are satellites above the earth, as I've observed them.  I don't think they are at the altitudes reported, however.

So why don't you measure their altitudes and stop just "thinking" about it? See: http://io9.com/5688939/how-to-measure-the-distance-from-the-earth-to-the-moon