Now that selective availability has been "turned off", are there any
pportunities for civilians who own an inexpensive handheld GPS receiver to
contribute to the National Geodetic Survey in terms of data collection,
either
for pay or on a voluntary basis?

The National Geodetic Survey manages the National CORS (Continuously
Operating Reference Station) system that enables positioning accuracies
approaching a few centimeters.  The sites in the CORS system, hence,
have rather sophisticated GPS receivers.  The removal of SA, while
beneficial to those who want to position points at the 10-meter level,
does not enable cm-level positioning with inexpensive receivers.