If your piezometers are open standpipes, they are self-correcting for settlement; the water level in the riser is the piezometric elevation. If they are pressure transducers, you are correct, you need to know the current elevation of the transducer and add the measured pressure, in feet or meters of water, to the tip elevation to get the piezometric elevation. You may be able to estimate the settlement at the tip elevation if you know the profile well enough. Otherwise, you have a problem, as the calculated piezometric elevations will be higher than actual.
As for the static condition, you may be able to go outside the influence of all construction and install one or more piezometers to get the natural static condition. If there is a sand layer below the clay, you could put a piezometer in the sand - it should be at static. The elevation of drainage ditches around the site might be another clue to the eventual static level.
Don't forget, as the load settles into the ground, it is bouyed up by the water table. When calculating the effective stress at the piezometer, correct for the change in density of the compressible soil and use the current elevation of the base of the load.