If I'm understanding correctly -
Panels 1/2 are in series with each other, as are 3/4, 5/6, 7/8, and 9/10...
Then these sets are connected in parallel, correct?
And when the 5/6 set is connected (in parallel) with the other sets, the power output drops?
IOW, when you disconnect 5 and 6, WITHOUT connecting the replacement panels, does power output increase?
If that's the case, they are essentially toast, although it looks like the damage to #6 may be minimal.
From my angle it looks like #5 took most of the hit, although since 5 and 6 are in series, they are both at fault and should be replaced.
This should be verifiable with an ammeter in series with the 5/6 set, between the panels and the rails. If the meter shows reverse current, then the blocking diode is fried at the very least. In addition, if they pull more than maybe 100mA or so, the panels themselves are leaking excessively and are pulling down the working panels, and probably themselves (which lines up with your low Isc measurements, particularly on panel 5).
As DanG pointed out, the sunlight/unloaded and shaded/loaded tests will also assist in confirming this as well, in addition to providing the temperatures. Just insert the ammeter between (for example) the positive from the 5/6 set and the positive rail, and run the light/shade tests. If it goes negative, note how much and compare notes.
If the results aren't obvious at that point, post 'em up; one of us can tell you what it means.
FWIW
Steve