> There are around two dozen satellites circling the globe and at any given time there will be six to ten visible

It's often better than that, nowadays. If I'm reading this GPS status page correctly, there are currently 29 active satellites. I just went outside and had 11 GPS plus 1 EGNOS above the horizon, so all 12 of my receivers could get busy. I wouldn't be surprised to see more than 12 in the almanac data.

I still lose signal in the woods, though.