> ...or is GPS just inherently less accurate for height than it is for 
> latitude/longitude?

Here is an article that could be helpful. It's about an upcoming GPS satellite 
reorg, but the pictures show how different lat/lon and vertical accuracies are. 
(Scroll down to Horizontal Accuracy and Vertical Accuracy.)

http://blogs.agi.com/navigationAccuracy/?p=315

Some explanation of the issues affecting altitude accuracy: 

http://weather.gladstonefamily.net/gps_elevation.html

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