A few random thoughts...
Is this system being powered by the PSU with the spikey output as discussed in another recent thread?
If it is, then some filter capacitors on the output of the power supply may help.
In your table of figures, the drift is worse at the start of the test.
Was the DVM switched on immediately before the first reading was taken?
Could the DVM suffer from warm up drift?
In your first post you state that you are looking for a resolution of 5cm in 50m, ie 0.1%
If you are using a 3 1/2 digit DVM, that has at best a resolution of 0.05%, when everything is taken into account in the DVM specification it could be far less accurate that you think. Even a Fluke.
Do you have a better DVM, maybe 4 1/2 digit, which you could try?
Noise on the signal could be a problem.
Try a simple RC low pass filter at the input of the DVM.
I would be inclined to try something with a 0.5s (or there abouts, not critical) time constant, and see if that makes a difference.
And finally, asking the blindingly obvious questions:
Was the pressure transmitter in the water?
Did the water level stay constant?
Were there any ripples (waves) on the water surface?
JimB
PS
Of course if everything else fails, you could always use the float valve recommended by Gary to keep the waterlevel in the dam constant.