How to repair solar panels without being able to source an exact replacement diode
The problem is that googling the chip markings produces no useful results

Not sure how your Google foo is then because, when I search "20S0045" I get:


DSS 25-0045A http://www.farnell.com/datasheets/123607.pdf

but that uses a different package (2 pins and a tab)


and I get:


SM74611 http://www.ti.com/lit/ds/symlink/sm74611.pdf

which is in a TO-263 which looks similar to a TO-252.


The "killer feature" of this SM74611 is that it has a forward voltage drop of only 26 mV at 8 A (I am curious how they can achieve that!).

These SM74611 can easily be ordered at Digikey or Mouser.

Since these SM74611 are much "better" (much lower forward voltage drop) than regular Schottky diodes I would really replace the faulty ones with the same model. Using a more "normal" diode will results in more voltage drop, resulting in more heat and a consequently reduces lifespan. In short: normal diodes will not last very long!