Okay, still missing some details - but I'll wade in with the information at hand. Static CPT is a great tool for identifying granular seams within moderate strength clays, BUT...
I've used CPT before (I worked for Fugro many moons ago) and I suspect that it won't work. Re-read the original question and note the "clay/shale" and "glacial till." I'm afraid that the cone will max out before reaching through the entire embankment, and will certainly max out in the first shale or glacial till strata it encounters. The embankment itself should be fairly uniform in material make-up, so CPT is unlikely to be of much help.
Your standpipe piezometers are entirely too large in diameter. They need to have an ID of 25 mm (and preferably less.) The pipe ID directly affects the piezometer's response. Put in new ones; keep the old ones for reference.
With dams, minor nuisances have a nasty habit of becoming major problems. Note that a movement of "only" 5 mm (about 0.2 inch) per year represents a total movement of 210 mm (about 8.3 inches) over 42 years, and a movement of "only" 12 mm (about 0.5 inch) per year represents a total movement of 504 mm (about 21.3 inches) in the life of the structure! The presence of the flume may have helped avoid a catastrophic failure - regular inspections picked up the concrete damage. Check the maintenance records to see how long the dam operator has been making repairs -
The previous comments regarding controlling the piezometric forces are absolutely correct; if possible, reduce the piezometric pressures first. Then you can look at other options if that doesn't work as desired.
Another word of caution. A total movement of 200 to 500 mm in a clay/shale can (will?) result in a degradation of shear strength along failure surface(s). A fairly rapid failure during a peak load event can occur under these circumstances...take advantage of the drought conditions to install instrumentation where it will be difficult to accomplish in wet periods.
Prepare an action plan to install mechanical dewatering to reduce the piezometric head - in case the weather (and dam) turn against you before you are entirely sure what is happening. You may have to install piezometers and dewatering wells "on the fly" in order to evaluate and reduce the excess piezometric head if the movement begins at an unexpected rate. Be sure to log the piezometer holes and wells - have an engineer or engineering geologist do this, not a technician.
Emergency repairs will be very stressful for both the field and office staff, but it will also be very rewarding professionally and personally. If emergency repairs become necessary, take advantage and use the time to build staff relationships and train your younger engineers. (I have some "fond" memories during repairs to Morris Sheppard Dam [Lake Possum Kingdom, Texas] - an Amberson-type dam. Imagine 300 mm holes drilled into a fractured clay shale beneath that dam that erupted into a lake-fed fountain over 3 meters high! This always seemed to happen late on Fridays...)
Let us know what you decide to do. Good luck!