Isn't there also an issue over the inherent errors being greater in altitude measurements due to the poorer intersection angles of the pseudo ranges vertically?
I seem to recall measuring all this many years ago, and concluding that because the vertical distance from the receiver to the SVs was so much smaller than the horizontal distance, due to the relatively low orbital height of the SVs, there were bound to be bigger spherical geometry errors in that plane.
IIRC I concluded then that the vertical accuracy could never be better than around 5 or 6 times the horizontal accuracy, unless using a stationary, phase measuring, survey type GPS receiver.
Vertical accuracy will also degrade faster, due to the need for really good visible SV geometry to maintain a reasonably good vertical pseudo range intersect angles.