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A satellite is either falling around Earth or falling to it, satellites don't just hover in one place. The best you could hope for would be a few satellites spaced out on an orbit that is inclined to line up with the SCP, maybe a highly elliptical ~24hr orbit with a low periapsis over the north pole and a very high apoapsis over the south pole so that they appear to pass through the SCP at exactly the same time each night. Then you could align using one of them for a split second at an exact time each night. Having the orbit highly elliptical would mean that maybe the satellite would be moving slowly enough as it passed through the SCP, at apoapsis, that it would be useable. I don't know the maths but an orbit with a period of 24hrs with a periapsis of about 500kms would surely have an apoapsis of around 80,000kms? Not sure about the parallax issues at that altitude? but I'm sure Charles is right.
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