So given the engineering politics of all this and a broken oversight system that enables and encourages inaction, let's forget Oroville completely for a moment.
Consider an imaginary dam exactly like Oroville as it is today - let's call it Sam's dam. I wave my magic wand and make you engineering Tsar (or Tsarina) of Sam's dam. No FERC, no Army Corps of Engineers, no DWR. All the dam operators and engineers report directly to you. You have a reasonable but generous budget. Qualifications like prudent, safe and reasonable are only subject to the consideration of your peers in the profession, not politicians or lawyers or anyone else.
So what do you do today about the possibility that the impervious layer is leaking today and/or the filter layer/drains might not be working right? If it was caused by differential settlement, can it be fixed? Has that ever been done anywhere else? What's the right course of action from a purely engineering standpoint?
You are going to have me give away some of my secrets... :-)
note: It is always best to first gather information from direct sources & get their viewpoints, past analysis, their opinions, any tests that have already been done, etc. Barring access to that important knowledge set....
(1) First, I would use military grade non-invasive spectral Thermal Infrared/Forward Looking Infrared TIR/FLIR camera mounted systems on a suitable aircraft to image map the thermal profile that the subsurface zone 3 layers of hydration leakage creates. I would also use concurrent digital stereo imaging to allow the overlay of the sets of TIR/FLIR captures.
(2) Second, I would contact the USGS or any group that has obtained inSAR satellite data in the past years and then arrange for an inSAR satellite data capture as soon as available. By doing an Interferometric synthesis of "two" periodic runs, you would be able to get to millimeter precision surface deformations of the entire surface of the Zone 3 embankment of the full dam downstream & crest regions.
(3) Third, I would collect samples of the Green Zone sediment and have a soils analysis performed to identify if there is a standout ratio of any marker component of the clay-clayey borrow pit area near the original pit by Oroville Airport.
(4) Fourth, I would identify if there were "clear" water flowing at locations in the green area and would capture H2O samples from the most direct flows to have analyzed for any indicative markers. Higher flow points may have better markers from deeper within.
(5) in items (3)(4) I would use a portable precision GPS units to mark the locations of sediment and H20 sample collection(s) and combine all of the collected data in an overlay map (1) through (5).
(6) I would go to the Grout Curtain Gallery Weir & collect sediment that has been present there and have it cross analyzed to any of the data to see if there are any trace minerals associated with (4)(5).
(7) I would obtain access to a group of about 3 seasoned experts who are in this unique field that I would choose myself from qualities I know what to look for. Also I would obtain access to construction experts who have experience in doing actual investigations and repairs of this specific situation. (always leverage expertise + it is the equivalent of a force multiplier, but choose carefully).
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At this point (1) thru (7), the data should give a good indicator to the magnitude of the hydration of the zone 3 fill, the extent, and possibly "mineral markers" to where the water source is from. There should be distinct mineral markers from the metavolcanic rock if the water source were flowing from or "porting" through the left abutment hillside. If all of the indicators point to an internal dam source path, OR, a strong hillside flow, then I would assess the possible "unknown" or unseeable phreatic percolation that may be deeper within the zone 3 fill. This "worst case" calculation would determine what actions or steps should be taken.
Earth Fill dams are fixable over any of these erosion path issues. The challenge for Oroville dam is its massive size. If there is belief that there may be a risk of a long term internal erosion flow, determining the exact location/location(s) would be take work. Differential Settlement (if proven the cause) creates "longitudinal" fracturing. To seal such a potentially wide horizontal type of region with probe injection of a clayey + bentonite mix would require knowing the origin(s) to an accurate degree.
Some dams were compromised in the core to the extent where they were excavated from the crest downward to the level of the defective layering and then they rebuilt the core with a modern clayey + bentonite mix. But that was done on smaller dams. Not as easy for the Oroville dam giant.
Perhaps the most difficult political decision (politics of engineering judgement) comes from a safety factor of unknowns. That is, making a decision to lower the reservoir below the threshold of the leaking area until an accurate assessment of the core & any suitable "fix/repair" is completed. Why would this decision be difficult? Because, in the real engineering world, you have to make decisions that are based upon a ratio of "belief verses proof". Proper engineering efforts will transition the mostly "I believe xyz" into "I now can prove xyz". The pressures when you are in the "belief" mostly side of the equation are enormous as the impact to this choice is challenged by those that demand "proof". You have to stand your ground. You also have to "build consensus" with powerful interests to get their trust that you know what you are doing.
OR, if you wanted to bypass (1) through (7), get a Canadair CL-415 fire fighting water bomber to unload dark green paint on the whole backside. Then nobody would know the difference. :-) /s