Based off of some quick and dirty calculations for a GPS satellite at approximately 20,000km above sea level, the difference in distance between a satellite directly overhead and one straight out over the horizon is around 5500km.

That's actually only about 18ms difference in delay. Unless there's something I'm failing to account for here, you should be able to get more than 0.1s precision based off of a single satellite's signal.

Subtract a flat ~75ms to account for the minimum delay (~66ms @ 20,000km) and half of the variable delay, and you shouldn't really be more than about 9ms out.

The distance to an overhead GPS satellite is somewhere in the range of .07-.09 light-seconds. The planet's width is basically irrelevant when your goal is .1 second accuracy.

If you're on Earth, you can assume that the satellite is closer than 30000 km or so. Light takes 0.1s to cross that distance.